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Geometric Solids

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A brief classification of basic geometric space figures
by Manny Macam

Published in: Education
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Geometric Solids

1. 1. GeometricSolidsPOLYHEDRANON-POLYHEDRA littlemakz2013
2. 2. LEONHARD EULER Leonhard Euler was a brilliant Swiss mathematician. He is often referred to as the “Beethoven of Mathematics”. littlemakz2013
3. 3. LEONHARD EULER Euler discovered an interesting relationship between the number of faces, vertices, and edges for any polyhedron. littlemakz2013
4. 4. POLYHEDRON POLYHEDRON POLYHEDRA – (pl. form) A polyhedron is a three-dimensional shape with flat faces. Each face is a polygons Platonic Solids Prisms Pyramids littlemakz2013
5. 5. POLYHEDRON Platonic Solids A platonic solid is a polyhedron all of whose faces are congruent regular convex polygons, and where the same number of faces meet at every vertex. Tetrahedron Hexahedron Octahedron Dodecahedron Icosahedron littlemakz2013
6. 6. POLYHEDRON Platonic Solids Tetrahedron • 3 triangles meet at each vertex • 4 Faces • 4 Vertices • 6 Edges littlemakz2013
7. 7. POLYHEDRON Platonic Solids Tetrahedron littlemakz2013
8. 8. POLYHEDRON Platonic Solids Hexahedron (Cube) • 3 squares meet at each vertex • 6 Faces • 8 Vertices • 12 Edges littlemakz2013
9. 9. POLYHEDRON Platonic Solids Hexahedron (Cube) littlemakz2013
10. 10. POLYHEDRON Platonic Solids Octahedron • 4 triangles meet at each vertex • 8 Faces • 6 Vertices • 12 Edges littlemakz2013
11. 11. POLYHEDRON Platonic Solids Octahedron littlemakz2013
12. 12. POLYHEDRON Platonic Solids Dodecahedron • 3 pentagons meet at each vertex • 12 Faces • 20 Vertices • 30 Edges littlemakz2013
13. 13. POLYHEDRON Platonic Solids Dodecahedron littlemakz2013
14. 14. POLYHEDRON Platonic Solids Icosahedron • 5 triangles meet at each vertex • 20 Faces • 12 Vertices • 30 Edges littlemakz2013
15. 15. POLYHEDRON Platonic Solids Icosahedron littlemakz2013
16. 16. POLYHEDRON Prism A prism is a polyhedron with two congruent polygonal bases and rectangular lateral faces. A prism has the same cross section all along its length Cube Rectangular Prism Triangular Prism Hexagonal Prism littlemakz2013
17. 17. POLYHEDRON Prism Cube • 6 Square Faces • 8 Vertices • 12 Edges littlemakz2013
18. 18. POLYHEDRON Prism Rectangular prism • 6 rectangular faces • 8 Vertices • 12 Edges littlemakz2013
19. 19. POLYHEDRON Prism Triangular prism • 2 triangular bases • 3 rectangular faces • 6 vertices • 9 edges littlemakz2013
20. 20. POLYHEDRON Prism Hexagonal prism • 2 hexagonal bases • 6 rectangular faces • 12 vertices • 18 edges littlemakz2013
21. 21. POLYHEDRON Pyramid A pyramid is a polyhedron with a polygonal base and triangular lateral faces. Triangular Pyramid Square Pyramid Pentagonal Pyramid littlemakz2013
22. 22. POLYHEDRON Pyramid Triangular pyramid • triangular-based • 3 congruent isosceles triangles littlemakz2013
23. 23. POLYHEDRON Pyramid Square pyramid • square-based • 4 congruent isosceles triangles littlemakz2013
24. 24. POLYHEDRON Pyramid Pentagonal pyramid • Pentagonal-based • 5 congruent isosceles triangles littlemakz2013
25. 25. NON-POLYHEDRON Three-dimensional shape associated with circles is called a non-polyhedron. No face of a non-polyhedron is a polygon. Cylinder Cone Sphere littlemakz2013
26. 26. NON-POLYHEDRONSPACE FIGURES Cylinder • 2 circular bases • Rectangular lateral surface littlemakz2013
27. 27. NON-POLYHEDRONSPACE FIGURES Cone • 1 circular base • lateral surface is a sector of a circle littlemakz2013
28. 28. NON-POLYHEDRONSPACE FIGURES Sphere • circular cross- section on any cut • largest circle passes through the center (great circle) littlemakz2013