Geometric Solids POLYHEDRONS NON-POLYHEDRONS

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

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

POLYHEDRON POLYHEDRON POLYHEDRA - pl. form) A polyhedron is a three-dimensional shape with flat faces. Each face is a polygons Platonic Solids Prisms Pyramids

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

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

POLYHEDRON Platonic Solids Tetrahedron

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

POLYHEDRON Platonic Solids Hexahedron (Cube)

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

POLYHEDRON Platonic Solids Octahedron

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

POLYHEDRON Platonic Solids Dodecahedron

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

POLYHEDRON Platonic Solids Icosahedron

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

POLYHEDRON Prism Cube 6 Square Faces 8 Vertices 12 Edges

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

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

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

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

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

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

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