Geometric Solids
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A brief classification of basic geometric space figures by Manny Macam
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Geometric Solids
- 1. Geometric Solids POLYHEDRA NON-POLYHEDRA littlemakz2013
- 2. LEONHARD EULER Leonhard Euler was a brilliant Swiss mathematician. He is often referred to as the “Beethoven of Mathematics”. littlemakz2013
- 3. LEONHARD EULER Euler discovered an interesting relationship between the number of faces, vertices, and edges for any polyhedron. littlemakz2013
- 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. 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. POLYHEDRON Platonic Solids Tetrahedron • 3 triangles meet at each vertex • 4 Faces • 4 Vertices • 6 Edges littlemakz2013
- 7. POLYHEDRON Platonic Solids Tetrahedron littlemakz2013
- 8. POLYHEDRON Platonic Solids Hexahedron (Cube) • 3 squares meet at each vertex • 6 Faces • 8 Vertices • 12 Edges littlemakz2013
- 9. POLYHEDRON Platonic Solids Hexahedron (Cube) littlemakz2013
- 10. POLYHEDRON Platonic Solids Octahedron • 4 triangles meet at each vertex • 8 Faces • 6 Vertices • 12 Edges littlemakz2013
- 11. POLYHEDRON Platonic Solids Octahedron littlemakz2013
- 12. POLYHEDRON Platonic Solids Dodecahedron • 3 pentagons meet at each vertex • 12 Faces • 20 Vertices • 30 Edges littlemakz2013
- 13. POLYHEDRON Platonic Solids Dodecahedron littlemakz2013
- 14. POLYHEDRON Platonic Solids Icosahedron • 5 triangles meet at each vertex • 20 Faces • 12 Vertices • 30 Edges littlemakz2013
- 15. POLYHEDRON Platonic Solids Icosahedron littlemakz2013
- 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. POLYHEDRON Prism Cube • 6 Square Faces • 8 Vertices • 12 Edges littlemakz2013
- 18. POLYHEDRON Prism Rectangular prism • 6 rectangular faces • 8 Vertices • 12 Edges littlemakz2013
- 19. POLYHEDRON Prism Triangular prism • 2 triangular bases • 3 rectangular faces • 6 vertices • 9 edges littlemakz2013
- 20. POLYHEDRON Prism Hexagonal prism • 2 hexagonal bases • 6 rectangular faces • 12 vertices • 18 edges littlemakz2013
- 21. POLYHEDRON Pyramid A pyramid is a polyhedron with a polygonal base and triangular lateral faces. Triangular Pyramid Square Pyramid Pentagonal Pyramid littlemakz2013
- 22. POLYHEDRON Pyramid Triangular pyramid • triangular-based • 3 congruent isosceles triangles littlemakz2013
- 23. POLYHEDRON Pyramid Square pyramid • square-based • 4 congruent isosceles triangles littlemakz2013
- 24. POLYHEDRON Pyramid Pentagonal pyramid • Pentagonal-based • 5 congruent isosceles triangles littlemakz2013
- 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. NON-POLYHEDRON SPACE FIGURES Cylinder • 2 circular bases • Rectangular lateral surface littlemakz2013
- 27. NON-POLYHEDRON SPACE FIGURES Cone • 1 circular base • lateral surface is a sector of a circle littlemakz2013
- 28. NON-POLYHEDRON SPACE FIGURES Sphere • circular cross- section on any cut • largest circle passes through the center (great circle) littlemakz2013