1. Geometric Solids
POLYHEDRONS
NON-POLYHEDRONS

2. LEONHARD EULER
Leonhard Euler was a brilliant Swiss mathematician. He is often referred to as the “Beethoven of Mathematics”.

3. LEONHARD EULER
Euler discovered an interesting relationship between the number of faces, vertices, and edges for any polyhedron.

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

5. Platonic Solids POLYHEDRON
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

6. Platonic Solids Tetrahedron POLYHEDRON 3 triangles meet at each vertex
4 Faces
4 Vertices
6 Edges

7. POLYHEDRON
Platonic Solids
Tetrahedron

8. Platonic Solids Hexahedron (Cube) POLYHEDRON
3 squares meet at each vertex
6 Faces
8 Vertices
12 Edges

9. POLYHEDRON
Platonic Solids
Hexahedron (Cube)

10. Platonic Solids Octahedron POLYHEDRON 4 triangles meet at each vertex
8 Faces
6 Vertices
12 Edges

11. POLYHEDRON
Platonic Solids
Octahedron

12. Platonic Solids Dodecahedron POLYHEDRON
3 pentagons meet at each vertex
12 Faces
20 Vertices
30 Edges

13. POLYHEDRON
Platonic Solids
Dodecahedron

14. Platonic Solids Icosahedron POLYHEDRON 5 triangles meet at each vertex
20 Faces
12 Vertices
30 Edges

15. POLYHEDRON
Platonic Solids
Icosahedron

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

17. POLYHEDRON
Prism
Cube
6 Square Faces
8 Vertices
12 Edges

18. Prism Rectangular prism POLYHEDRON 2 Square Bases 4 rectangular faces
8 Vertices
12 Edges

19. Prism Triangular prism POLYHEDRON 2 Triangular Bases
3 rectangular faces
6 Vertices
9 Edges

20. POLYHEDRON
Pyramid
A pyramid is a polyhedron with a polygonal base and triangular lateral faces.
Polygonal Pyramid
Square Pyramid
Triangular Pyramid

21. NON-POLYHEDRON
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
Cylinder
Cone
Sphere

22. SPACE FIGURES Cylinder NON-POLYHEDRON 2 circular bases Rectangular
lateral surface

23. SPACE FIGURES Cone NON-POLYHEDRON 1 circular bases
lateral surface is a sector of a circle

24. SPACE FIGURES Sphere NON-POLYHEDRON circular cross-section on any cut
largest circle passes through the center (great circle)