What are the characteristics of the Archimedean solids?

Answer 1

Here is some information about the 13 Archimedean solids:

Tetrahedron-related:

1) The truncated tetrahedron has 12 vertices, 18 edges, & 8 faces (4 triangles & 4 hexagons).

Cube-related:

2) The truncated cube has 24 vertices, 36 edges, & 14 faces (8 triangles & 6 octagons). Also known as a truncated hexahedron.

3) The truncated octahedron has 24 vertices, 36 edges, & 14 faces (6 squares & 8 hexagons).

4) The cuboctahedron has 12 verticies, 24 edges, & 14 faces (8 triangles & 6 squares).

5) The small rhombicuboctahedron has 24 vertices, 48 edges, & 26 faces (8 triangles & 18 squares). Also known simply as a rhombicuboctahedron.

6) The great rhombicuboctahedron has 48 vertices, 72 edges, & 26 faces (12 squares, 8 hexagons, & 6 octagons). Also known as a truncated cuboctahedron.

7) The snub cube has 24 vertices, 60 edges, & 38 faces (32 triangles & 6 squares). Also known variously as a snub hexahedron, snub octahedron, or snub cuboctahedron. This shape, along with the snub dodecahedron, has 2 chiral forms.

Icosahedron-related:

8) The truncated icosahedron has 60 vertices, 90 edges, & 32 faces (12 pentagons & 20 hexagons). Also known as a buckyball or a football/soccer ball.

9) The truncated dodecahedron has 60 vertices, 90 edges, & 32 faces (20 triangles & 12 decagons).

10) The icosidodecahedron has 30 vertices, 60 edges, & 32 faces (20 triangles & 12 pentagons).

11) The small rhombicosidodecahedron has 60 vertices, 120 edges, & 62 faces (20 triangles, 30 squares, & 12 pentagons). Also known simply as a rhombicosidodecahedron.

12) The great rhombicosidodecahedron has 120 vertices, 180 edges, & 62 faces (30 squares, 20 hexagons, & 12 decagons). Also known as a truncated icosidodecahedron.

13) The snub dodecahedron has 60 vertices, 150 edges, & 92 faces (80 triangles & 12 pentagons). Also known as a snub icosahedron or a snub icosidodecahedron. This shape, along with the snub cube, has 2 chiral forms.