Snub square antiprism

In geometry, the snub square antiprism is one of the Johnson solids (J85).

It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids, although it is a relative of the icosahedron that has fourfold symmetry instead of threefold.

It can also be constructed as a square gyrobianticupolae, connecting two anticupolae with gyrated orientations.

Construction
The snub square antiprism is constructed as its name suggests, a square antiprism which is snubbed, and represented as ss{2,8}, with s{2,8} as a square antiprism.

It can also be constructed in Conway polyhedron notation as sY4 (snub square pyramid).

Snub antiprisms
Similarly constructed the ss{2,6} is a snub triangular antiprism (a lower symmetry octahedron), and result as a regular icosahedron. A snub pentagonal antiprism, ss{2,10}, or higher n-antiprisms can be similar constructed, but not as a convex polyhedron with equilateral triangles. The preceding Johnson solid, the snub disphenoid also fits constructionally as ss{2,4}, but you have to retain two degenerate digonal faces (drawn in red) in the digonal antiprism.

References

External links

Category:Johnson solids