# The Icosidodecahedron

A semi-regular polyhedron with two triangles and two pentagons alternating around each vertex.

The icosidodecahedron is one of the thirteen archimedian solids. It can be created by slicing suitable sections off the vertices of either a dodecahedron or an icosahedron and thus may be inscribed in either solid.

Vertex Symbol |
Wythoff Symbol |
No. of Vertices |
No. of Edges |
{3} Faces |
{5} Faces |
Symmetry Group |
Dual Polyhedron |

3.5.3.5 | 2 | 3 5 | 30 | 60 | 20 | 12 | A_{5}×C_{2} |
Rhombic Triacontahedron |

Edge ratios:

- `e/rho = 2tan(18^@)=2sqrt((5-2sqrt(5))/5)`
- `e/R = (sqrt(5)-1)/2`
- `e/(e_12) = (1+sqrt(5))/4`
- `e/(e_20) = 1/2`

where `e` is the edge length, `rho` is the inter-radius, `R` is the circum-radius, `e_12` is the edge of the circumscribing dodecahedron, and `e_20` is the edge of the circumscribing icosahedron.