This document discusses crystallography and crystal structure. It defines key terms like crystalline solids, amorphous solids, unit cell, crystal lattice, crystallographic planes, and Miller indices. It describes the seven crystal systems (cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, trigonal) based on their symmetry characteristics. It also discusses crystal forms, symmetry operations like rotation axes and planes of symmetry, and the notation used to describe crystal planes and orientations.
An Introduction to Crystallography, Elements of crystals crystal systems: Cubic (Isometric) System,Tetragonal System, Orthorhombic System, Hexagonal System; Trigonal System, Monoclinic System, Triclinic System
An Introduction to Crystallography, Elements of crystals crystal systems: Cubic (Isometric) System,Tetragonal System, Orthorhombic System, Hexagonal System; Trigonal System, Monoclinic System, Triclinic System
Solid state chemistry- laws of crystallography- Miller indices- X ray diffraction- Bragg equation- Spectrophotometer- Determination of interplanar distance- Types of crystal
NANO106 is UCSD Department of NanoEngineering's core course on crystallography of materials taught by Prof Shyue Ping Ong. For more information, visit the course wiki at http://nano106.wikispaces.com.
Space lattice, Unit cell, Bravais lattices (3-D), Miller indices, Lattice planes, Hexagonal closed packing (hcp) structure, Characteristics of an hcp cell, Imperfections in crystal: Point defects (Concentration of Frenkel and Schottky defects).
X – ray diffraction : Bragg’s law and Bragg’s spectrometer, Powder method, Rotating crystal method.
Solid state chemistry- laws of crystallography- Miller indices- X ray diffraction- Bragg equation- Spectrophotometer- Determination of interplanar distance- Types of crystal
NANO106 is UCSD Department of NanoEngineering's core course on crystallography of materials taught by Prof Shyue Ping Ong. For more information, visit the course wiki at http://nano106.wikispaces.com.
Space lattice, Unit cell, Bravais lattices (3-D), Miller indices, Lattice planes, Hexagonal closed packing (hcp) structure, Characteristics of an hcp cell, Imperfections in crystal: Point defects (Concentration of Frenkel and Schottky defects).
X – ray diffraction : Bragg’s law and Bragg’s spectrometer, Powder method, Rotating crystal method.
Crystallography and X-ray diffraction (XRD) Likhith KLIKHITHK1
Atoms in materials are arranged into crystal structures and microstructures.
Periodic arrangement of atoms depends strongly on external factors such as temperature, pressure, and cooling rate during solidification. Solid elements and their compounds are classified into amorphous, polycrystalline, and single crystalline materials. The amorphous solid materials are isotropic in nature because their atomic arrangements are not regular and possess the same properties in all directions. In contrast, the crystalline materials are anisotropic because their atoms are arranged in regular and repeated pattern, and their properties vary with direction. The polycrystalline materials are combinations of several crystals of varying shapes and sizes. The properties of polycrystalline materials are strongly dependent on distribution of crystals sizes, shapes, and orientations within the individual crystal. Diffraction pattern or intensities of X-ray diffraction techniques are used for characterizing and probing arrangement of atoms in each unit cell, position of atoms, and atomic spacing angles because of comparative wavelength of X-ray to atomic size.The X-ray diffraction, which is a non-destructive technique, has wide range of material analysis including minerals, metals, polymers, ceramics, plastics, semiconductors, and solar cells. The technique also has wide industry application including aerospace, power generation, microelectronics, and several others. The X-ray crystallography remained a complex field of study despite wide industrial applications.
In this lecture , the focus is on geological aspects of minerals. We are going to discuss about the crystal symmetry of minerals,axis of rotation , axis of rotoinversion symmetry y, and mirror plane. The crystal classes may be sub-divided into one of 6 crystal systems namely Triclinic, monoclinic, orthorhombic, tetragonal, hexagonal and isometric (cubic).
Crystallographic axis
The identification of specific symmetry operations enables one to orientate a crystal according g to an imaginary set of reference lines known as the crystallographic axis.With the exception of the hexagonal system, the axes are designated designated The ends of each a, b, and c. The ends of each axes are designated axes are designated + or -. This is important for the derivation of Miller Indices.
about the formation and causes and impacts of the cyclone formation in the earth. and cyclone formed in the INDIA region whole about the briefly explained about cyclone
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
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2. Matter
• Any substance which has mass and occupies space
• All physical objects are composed of matter.
3. Solids:
• Objects with definite size and shape are
known as solids.
• Incompressible, Rigid, Mechanically
strong, Atoms are closely packed.
Liquids & Gases:
• Atoms or molecules are not fixed and
cannot form any shape and size. They gain
the shape and size of the container.
• Atoms are loosely packed.
4. i) Crystalline Solids:
The solids in which atoms or molecules are arranged in a
regular and orderly manner in three dimension are called
Crystalline Solids.
Ex: i) Metallic: Gold, Silver, Aluminium
ii) Non-Metallic: Diamond, Silicon,
Quartz,Graphite etc.,
Solids are classified into two categories
5. ii) Amorphous Solids
The solids in which atoms or molecules are not arranged in
a regular and orderly manner in three dimension are called
Amorphous Solids
Ex: Glass, Plastic, rubber
6.
7. Crystalline Solids Amorphous Solids
1.Atoms or molecules have regular periodic
arrangements
2.They are anisotropic in nature.
3. They exhibit directional properties.
4.They have sharp melting points.
5. Crystal breaks along regular crystal planes and
hence the crystal pieces have regular shape
Ex: Copper, Silver, Aluminium etc
Atoms or molecules are not arranged in a regular
periodic manner. They have random arrangement.
They are isotropic in nature.
They do not exhibit directional properties.
They do not possess sharp melting points
Amorphous solids breaks into irregular shape due to
lack of crystal plane.
Ex: Glass, Plastic, rubber, etc.
Differences between
Crystalline solid and
Amorphous solid
9. Crystal lattice (Space lattice)
Defined as 3-dimensional array of points are spatially arranged in
specific pattern.
Or
It is geometric arrangement of matters (atoms, ions, molecules)
Characters of lattice
10.
11.
12. Unit Cell
• The smallest possible portion or geometrical figure
of crystal lattice and which buildup by repetition in
three dimensions, is called unit cell.
(or)
• It is a fundamental elementary pattern.
• This unit cell is basic structural unit or building
blocks of the crystal structure
14. UNIT CELL TYPESUNIT CELL TYPES
Primitive lattice (P)
Centered lattice (I):
• Primitive lattice (P) :
In this lattice the unit cell
consists of eight corner
atoms.
15. Centered lattice (I):
• Body Centered Unit Cells
• Face Centered Unit Cells
• End Centered Unit Cells
Body Centered Unit Cells(B)
17. • Base Centered lattice (C):
• In this lattice along with the corner atoms,
the base and opposite face will have centre
atoms
18.
19. Crystal Element Face
Edge
Solid angle
These 3 crystal elements be an a mathematical relationship is called a Euler’s Formula
Euler’s formula is F + A=E+2
22. The angle found between a pair of adjacent faces of a crystal..
Interfacial angle
23. Crystal Symmetry
It explains how similar atoms or group of
atoms (motif) repeated symmetrically in
space to produce ordered structure .
It can be studied with the help of operation
than can be operated on the crystals known as
Symmetry Operation
24. Symmetry operation
Is an operation that can be performed either physically or
imaginatively on crystal with reference to Plane, Axis, Point
within its mass.
Symmetry operation achieved by
•Rotating the crystal in particular axis
•Select the plane which shows mirror image
•Select the point which shows equidistance
25.
26.
27.
28. This is a line about which the crystal may be rotated so as to show the same view
of the crystal more than once per rotation.
29. There are four axis of symmetry :-
• On the rotation about the axis, if the same faces or same view occurs 2 times, the axis termed
as Diad axis or two fold axis. D:2fold.avi
• On the rotation about the axis, , if the same faces or same view occurs 3 times, the axis termed
as Triad axis or three fold axis. D:3 fold.avi
• On the rotation about the axis, if the same faces or same view occurs 4 times, the axis termed as
Tetrad axis or four fold axis. D:4 fold.avi
• On the rotation about the axis, , if the same faces or same view occurs 6 times, the axis termed
as Hexad axis or six fold axis.
30. Symmetry CharactersSymmetry Characters
Centre of SymmetryCentre of Symmetry Plane of SymmetryPlane of Symmetry Axes of SymmetryAxes of Symmetry
PresentPresent 0909
II fold axesII fold axes III fold axesIII fold axes IV fold axesIV fold axes VI fold axesVI fold axes
0606 0404 0303 --
31. Centre of Symmetry:-
It is a imaginary point in the crystal that any line drawn
through it intersects the surface of the crystal at equal
distance on either side
Center of symmetry is the point from
which all similar faces are
equidistant.
33. Crystal System or Lattice system:
Crystal system refers to Geometry of crystal and crystal structure and
which can be described by set of reference axes (crystallographic axes) .
Types Of Crystal System
34.
35. ISOMETRIC OR CUBIC SYSTEM
Symmetry CharactersSymmetry Characters
Centre of SymmetryCentre of Symmetry
Plane of
Symmetry
Plane of
Symmetry
Axes of SymmetryAxes of Symmetry
PresentPresent 0909
II fold axesII fold axes III fold axesIII fold axes IV fold axesIV fold axes VI fold axesVI fold axes
0606 0404 0303 --
36. TETRAGONAL CRYSTAL SYSTEMS
Symmetry CharactersSymmetry Characters
Centre of SymmetryCentre of Symmetry
Plane of
Symmetry
Plane of
Symmetry
Axes of SymmetryAxes of Symmetry
PresentPresent 0505
II fold axesII fold axes III fold axesIII fold axes IV fold axesIV fold axes VI fold axesVI fold axes
0404 -- 0101 --
37. ORTHORHOMBIC CRYSTAL SYSTEMS
Symmetry CharactersSymmetry Characters
Centre of SymmetryCentre of Symmetry
Plane of
Symmetry
Plane of
Symmetry
Axes of SymmetryAxes of Symmetry
PresentPresent 0303
II fold axesII fold axes III fold axesIII fold axes IV fold axesIV fold axes VI fold axesVI fold axes
0303 -- -- --
38. MONOCLINIC CRYSTAL SYSTEMS
Symmetry CharactersSymmetry Characters
Centre of
Symmetry
Centre of
Symmetry
Plane of
Symmetry
Plane of
Symmetry
Axes of SymmetryAxes of Symmetry
PresentPresent 0101
II fold
axes
II fold
axes
III fold
axes
III fold
axes
IV fold
axes
IV fold
axes
VI fold
axes
VI fold
axes
0101 -- -- --
39. TRICLINIC CRYSTAL SYSTEMS
Symmetry CharactersSymmetry Characters
Centre of
Symmetry
Centre of
Symmetry
Plane of
Symmetry
Plane of
Symmetry
Axes of SymmetryAxes of Symmetry
PresentPresent --
II fold axesII fold axes
III fold
axes
III fold
axes
IV fold
axes
IV fold
axes
VI fold
axes
VI fold
axes
-- -- -- --
40. HEXAGONAL CRYSTAL SYSTEMS
Symmetry CharactersSymmetry Characters
Centre of SymmetryCentre of Symmetry
Plane of
Symmetry
Plane of
Symmetry
Axes of SymmetryAxes of Symmetry
PresentPresent 0707
II fold axesII fold axes III fold axesIII fold axes IV fold axesIV fold axes VI fold axesVI fold axes
0606 -- -- 0101
Symmetry Characters(trigonal)Symmetry Characters(trigonal)
Centre of SymmetryCentre of Symmetry
Plane of
Symmetry
Plane of
Symmetry
Axes of SymmetryAxes of Symmetry
PresentPresent 0303
II fold axesII fold axes III fold axesIII fold axes IV fold axesIV fold axes VI fold axesVI fold axes
0303 0101 -- ----
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55. CRYSTALLOGRAPHIC PLANES
z
x
y
a b
c
Crystal plane may be defined as imaginary plane (or indeed any
parallel plane) in the crystal which intersects the main
crystallographic axes of the crystal
56. CRYSTALLOGRAPHIC NOTATION
Crystallographic notation is the method or symbolic representation
of relationship of any crystal face to crystallographic axes .
This crystallographic notation system can be explained by two
methods.
• Weiss parameter
• Miller indices
57. WEISS PARAMETER (Weiss notation/ Weiss indices)
These are the relative numbers of at which given crystal face cuts
the crystallographic axes.
Or
The distance from the origin at which crystal face intercept the
crystallographic axes.
z
x
y
a b
c
58. The most general expression for Weiss parameter is
na:mb:pc
Where n, m, p are the length cut off by the face on the a, b, & c axes
respectively
59. • Miller Indices are a symbolic representation for the orientation of plane in a
crystal & are defined as the reciprocals of the fractional intercepts
which the plane makes with the crystallographic axes.
• Most common Millerian symbol is h,k,l
60. To find the Miller indices of a plane, take the following steps:
1. Determine the intercepts of the plane along each of the three crystallographic
directions.
2. Take the reciprocals of the intercepts.
3. If fractions result, multiply each by the denominator of the smallest fraction.
61. 61
CRYSTALLOGRAPHIC PLANES
example a b c
z
x
y
a b
c
4. Miller Indices (200)
1. Intercepts 1/2 ∞ ∞
2. Reciprocals 1/½ 1/∞ 1/∞
2 0 0
3. Reduction 2 0 0
z
x
y
a b
c
4. Miller Indices (110)
1. Intercepts 1 1 ∞
2. Reciprocals 1/1 1/1 1/∞
1 1 0
3. Reduction 1 1 0
example a b c
62. 62
Axis X Y Z
Intercept
points 1 ∞ ∞
Reciprocals 1/1 1/ ∞
1/
∞
Smallest Ratio 1 0 0
Miller İndices (100)
Example-1
(1,0,0)
63. 63
Axis X Y Z
Intercept points 1 1 ∞
Reciprocals 1/1 1/ 1 1/ ∞
Smallest Ratio 1 1 0
Example-2
(1,0,0)
(0,1,0)
64. 64
Axis X Y Z
Intercept points 1 1 1
Reciprocals 1/1 1/ 1 1/ 1
Smallest Ratio 1 1 1
(1,0,0)
(0,1,0)
(0,0,1)
Example-3
65. 65
Axis X Y Z
Intercept points 1/2 1 ∞
Reciprocals 1/(½) 1/ 1 1/ ∞
(1/2, 0, 0)
(0,1,0)
Example-4
66.
67. Crystal formA crystal form is a set of crystal faces that are related to each other by symmetry.
Types of crystal form
Crystal forms are broadly classified into two types
1. Closed Forms 2. Open Forms
68. There are 48 possible forms, those are mainly classified as
1.Common form in non-isomeric system (38)
2.Common form in isometric system(10)
70. Common form in isometric system
1. Hexahedron or cube
2. Dodecahedron (rhombic dodecahedron)
3. Octahedron
4. Tetra hexahedron
5. Trapezohedron
6. Tetrahedron
7. Gyroid
8. Pyritohedron
9. Diploid
10. Tetartoid
71.
72.
73.
74. 1. Pyramids(7) Trigonal pyramid: Ditrigonal pyramid: Rhombic pyramid: Tetragonal pyramid:
Ditetragonal pyramid: Hexagonal pyramid; Dihexagonal pyramid:
Rhombic pyramid:
A pyramid is a open form composed 3, 4, 6, 8 or 12 non-parallel face, where all faces in the form
meet at common point and each face intersect all three crystallographic axis
75. Trigonal pyramid: Ditrigonal pyramid: Rhombic pyramid: Tetragonal pyramid:
Ditetragonal pyramid: Hexagonal pyramid; Dihexagonal pyramid:
Trigonal pyramid: 3-faced form where all faces are
related by a 3-fold rotation axis.
Ditrigonal pyramid: 6-faced form where all faces are
related by a 3-fold rotation axis.
76. Trigonal pyramid: Ditrigonal pyramid: Rhombic pyramid: Tetragonal pyramid:
Ditetragonal pyramid: Hexagonal pyramid; Dihexagonal pyramid:
Rhombic pyramid: 4-faced form where the faces are related by
mirror planes..
Tetragonal pyramid: 4-faced form where the faces are related by a 4
axis. In the drawing the small triangular faces that cut the corners
represent the tetragonal pyramid.
77. Ditetragonal pyramid: 8-faced form where all faces are related
by a 4 axis. In the drawing shown here, the upper 8 faces belong to
the ditetragonal pyramid form.
• Hexagonal pyramid: 6-faced form where all faces
are related by a 6 axis. If viewed from above, the
hexagonal pyramid would have a hexagonal shape.
• Dihexagonal pyramid: 12-faced form where all faces are
related by a 6-fold axis. This form results from mirror planes
that are parallel to the 6-fold axis.
78. pyramids or Bipyramids(7)
Trigonal dipyramid: Ditrigonal dipyramid: Rhombic dipyramid
Tetragonal dipyramid: Ditetragonal dipyramid: Hexagonal dipyrami
Dihexagonal dipyramid:
Rhombic dipyramid:
Dipyramids are closed forms consisting of 6, 8, 12, 16, or 24 faces.
Dipyramids are pyramids that are reflected across a mirror plane.
83. Trigonal prism: 3 - faced form with all faces parallel to a 3 -fold
rotation axis
Trigonal prism: Ditrigonal prism: Rhombic prism: Tetragonal prism: Ditetragonal
prism: Hexagonal prism: Dihexagonal prism:
Ditrigonal prism: 6 - faced form with all 6 faces parallel to a
3-fold rotation axis. i.e. it does not have 6-fold rotational
symmetry.
84. Rhombic prism: 4 - faced form with all faces parallel to a line
that is not a symmetry element. In the drawing to the right, the 4
shaded faces belong to a rhombic prism.
Trigonal prism: Ditrigonal prism: Rhombic prism: Tetragonal prism: Ditetragonal
prism: Hexagonal prism: Dihexagonal prism:
Tetragonal prism: 4 - faced open form with all faces parallel to a
4-fold rotation axis. The top and bottom faces make up the a form
called the top/bottom pinacoid.
85. Trigonal prism: Ditrigonal prism: Rhombic prism: Tetragonal prism: Ditetragonal
prism: Hexagonal prism: Dihexagonal prism:
• Ditetragonal prism: 8 - faced form with all faces parallel to
a 4-fold rotation axis. In the drawing, the 8 vertical faces
make up the ditetragonal prism.
• Hexagonal prism: 6 - faced form with all faces parallel to
a 6-fold rotation axis. Again the faces on top and bottom
are the top/bottom pinacoid form.
86. Dihexagonal prism: 12 - faced form with all faces parallel to a 6-
fold rotation axis. Note that a horizontal cross-section of this model
would have apparent 12-fold rotation symmetry. The dihexagonal
prism is the result of mirror planes parallel to the 6-fold rotation axis.
Trigonal prism: Ditrigonal prism: Rhombic prism: Tetragonal prism: Ditetragonal prism:
Hexagonal prism: Dihexagonal prism:
91. Common form in isometric system
1. Hexahedron or cube
2. Dodecahedron (rhombic dodecahedron)
3. Octahedron
4. Tetra hexahedron
5. Trapezohedron
6. Tetrahedron
7. Gyroid
8. Pyritohedron
9. Diploid
10. Tetartoid
92. Hexahedron or cube
A hexahedron is a general form with 6 squares at 900
angle to
each other. Each faces intersection crystallographic axis and
parallel to others. 4-fold axes are perpendicular to the face of
the cube.
Octahedron
An octahedron is an 8-faced form, faces are equilateral triangle
shape, and these are meeting at common point. That results
form a three 4-fold axes with perpendicular mirror planes.
Common form in isometric system
93.
Dodecahedron (rhombic dodecahedron)
A dodecahedron is a closed 12- rhomb shape faced form. Each
faces intersect two crystallographic axes are parallel to other one
axis.
Tetra hexahedron
The tetra hexahedron is a 24-isosceles triangular faced form with all
faces are parallel to one of the a axes, and intersect the other 2 axes
at different lengths.
Common form in isometric system
94. Trapezohedron
An isometric trapezohedron is a 12-faced closed form with all faces
intersect two of the a axes at equal length and intersect the third
a axis at a different length.
Tetrahedron
The tetrahedron is a form composed 4equilateral triangular
faces, each of which intersects all the three crystallographic axes
at equal lengths.
Common form in isometric system
95. Gyroid
A gyroid is a form in the crystal that has note no mirror planes and
This form has no center of symmetry.
Pyritohedron
The pyritohedron is a 12-faced form that occurs in the crystal and
each of the faces that make up the form have 5 sides.
Common form in isometric system
96. Diploid
The diploid is the general form for the diploid.
Tetartoid
Tetartoids are general forms in the tetartoidal class which only
has 3-fold axes and 2-fold axes with no mirror planes.
Common form in isometric system