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Quasi Crystalline Geometry for Architectural Structures Barbara Weinzierl 1)*  and Ture Wester 2) 1) Stud. Arch.  2) Associate Professor Royal Danish Academy of Fine Arts, School of Architecture, Copenhagen, Denmark.
Electron-microscope Picture of a Quasi-Crystal Diffraction Pattern with a 10-fold / 5-fold Symmetry
Roger Penrose and  One of his Patterns
Two Aperiodic Penrose Patterns with 5-fold Symmetry The Pattern is made of two different Golden Diamond Shaped tiles
How to build the  Golden  Fat and Thin Rhombohedra. All facetts  have the  Golden Ratio
This Penrose Pattern consists of Eight different possible combinations of Golden Diamond Tiles. Those eight combinations are called Vertex Stars.
Penrose Structure
Double Layer Quasi-crystal Structure Double Layer ->  nodes in six different heights
The Binary Substitution
Binary Substitution Tiling Decomposition of Prototiles
Binary Substitution Structures
The Rhombic Dodecahedron, The Rhombic Icosahedron, The Rhombic Triacontahedron, and how to make them...
...and how to cluster them
Golden Rhombic Triacontahedra  attached to one  Golden Rhombic Triacontahedron  in the core  in a 5-fold Symmetry
Gaps filled up  with single Golden Rhombi offering possibilities  for attaching  more  Golden Rhombic Triacontahedra
Clustering with  Golden Rhombic Dodecahedra, Golden Rhombic Icosahedra, and Golden Rhombic Triacontrahedra...
… and filling up with some more single Golden Rhombi
… Fractals or another mistake...
Graphically possible: making a  Binary Substitution of a Binary Substitution  of a Binary Substituition…
...Structurally not possible without  periodic parts
The Principle  of how to stabilize those structures
 
One way of stabelizing a Double Layer Quasi Crystal Spaceframe
One way of stabilizing a  Golden Rhombic Triacontahedron starting with  a stable core and with the other  additional structrual elements  in a band around and through the structure
Possibilities for a building? Observe the 5 parallel plates  for possible floors!
 
 
Chaos?
 
 
 
Single Layer  QC Polyhedron
One Layer Bubble  with all facetts closed  with stiff plates or made of stiff frames is stable
Another way of stabilizing
Single Layer QC Domes may be stabilized by a Torus Ring at the free Edge if all Meshes are Plate stabilized
Existing Examples of Artistic influenced Structures and Architecture
Quasi Crystal  Sculptur at the DTU Danish Technical University in Copenhagen, Denmark by Tony Robbin
 
 
The RMIT Storey Hall in Melbourne, Australia
 
Foyer and  Auditory
London Stanstead Airport
 
 
Airport Stuttgart
 
 
 
 
Skavsta Terminal Deconstruction across Dimensions
 
 
 
 
 
…  further search for a  Fractal
 
 
 
 
 
Departure Hall
 
 
 
 
 
 
 
Arrival Hall
 
 
 
 
 
 
 
 
 
Train Station
 
 
Coach Station
 
 
 
 
Tower
 
 
The End (for now)

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Diploma thesis project presentation