Solids - Vertices Edges and Faces - CONVEX POLYHEDRON
Archimedean Solid
... 13 convex polyhedra use regular polygons as faces, possibly using for than one shape.
Convex Polyhedron
... a solid made of flat faces, where a line can cut the polyhedron in at most 2 places
Concave Polyhedron
... a solid made of flat faces, where a line can cut the polyhedron in more than 2 places
Snub
... faces are shrunk (maintaining shape but not orientation) and new polygons added to edges
Platonic Solids
... five regular polyhedron (all edges are equal, all faces are the same regular polygons)
Face
... flat surface of a polyhedron
Truncate
... remove a vertex to create a new face
Edge
... sharp line formed where two surfaces (faces) meet
Vertex
... the point where 3 or more edges meet
Definition: [3-5-3-5]
A Polyhedron with each vertex made from triangle-pentagon-triangle-pentagon around the point. (Icosidodecahedron)
F: 6 squares V: 8 E: 12
Cube [6-6-6]
F: 8 triangles + 6 squares E: 24 V: 12
Cuboctahedron [3-4-3-4]
F: 20 triangles + 12 pentagons E: 60 V: 30
Icosidodecahedron [3-5-3-5]
F: 12 pentagons V: 20 E: 30
Regular Dodecahedron [5-5-5]
F: 20 equilateral triangles V: 12 E: 30
Regular Icosahedron [3-3-3-3-3]
F: 8 equilateral triangles V: 6 E: 12
Regular Octahedron [3-3-3-3]
F: 4 equilateral triangles V: 4 E: 6
Regular Tetrahedron [3-3-3]
F: 8 triangles + 18 squares E: 48 V: 24
Rhombiccubotahedron [3-4-4-4]
F: 20 triangles + 30 squares + 12 pentagons E: 120 V: 60
Rhombicosidodecahedron [3-4-5-4]
F: 32 triangles + 6 squares E: 60 F: 24
Snub Cube [3-3-3-3-4]
F: 80 triangles + 12 pentagons E: 150 V: 60
Snub Dodecahedron [3-3-3-3-5]
F: 8 triangles + 6 octagons E: 36 V: 24
Truncated Cube [3-8-8]
F: 12 squares + 8 hexagons + 6 octagons E: 72 V: 48
Truncated Cuboctahedron [4-6-8]
F: 20 triangles + 12 decagons E: 90 V: 60
Truncated Dodecahedron [3-10-10]
F: 12 pentagons + 20 hexagons E: 90 F: 60
Truncated Icosahedron [5-6-6] (football/soccer ball)
F: 30 squares + 20 hexagons + 12 decagons E: 180 V: 120
Truncated Icosidodecahedron [4-6-10]
F: 6 squares + 8 hexagons E: 36 V: 24
Truncated Octahedron [4-6-6]
F: 4 triangles + 4 hexagons E: 18 V: 12
Truncated Tetrahedron [3-6-6]
Eulers formula for Polyhedra
V + F - E = 2 (Convex solids 2)
