The compound of five icosahedra is uniform polyhedron compound. It's composed of 5

icosahedra In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetri ...

, rotated around a common axis. It has icosahedral symmetry ''I_h''. The triangles in this compound decompose into two orbits under action of the symmetry group: 40 of the triangles lie in coplanar pairs in icosahedral planes, while the other 60 lie in unique planes.

Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the cyclic permutations of : (0, ±2, ±2τ) : (±τ⁻¹, ±1, ±(1+τ²)) : (±τ, ±τ², ±(2τ−1)) where τ = (1+)/2 is the

golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( ...

(sometimes written φ).

References

*. Polyhedral compounds {{polyhedron-stub