|Bowers style acronym||Pyrike|
|Faces||12 isosceles triangles, 8 triangles|
|Vertex figure||Mirror-symmetric pentagon|
|Measures (edge length 1)|
|Conjugate||Pyritohedral great icosahedron|
|Symmetry||B3/2, order 24|
The pyritohedral icosahedron, pyrike, or snub truncated octahedron is a convex isogonal polyhedron that is a variant of the icosahedron with pyritohedral symmetry. It has 8 equilateral triangles and 12 isosceles triangles for faces.
It can generally be formed by alternating a semi-uniform truncated octahedron.
This polyhedron can be formed as the hull of three orthogonal rectangles. The short edges of these rectangles then become the set of 6 edges of this polyhedron. If the rectangles have short edges of length a and long edges (now internal to the polyhedron) of length b, the remaining 24 edges of the polyhedron have length . In particular if the rectangles are golden rectangles (that is, b is times greater than a) it gives the regular icosahedron.
A particular case of this polyhedron, where the 24 edges of the equilateral triangles have length and the remaining 6 edges have length , appears as the alternation of the uniform truncated octahedron.
Another case of this polyhedron, with 6 unit edges and 24 of length , can be obtained by removing the 8 vertices of an inscribed cube from a regular dodecahedron.
External links[edit | edit source]
- Klitzing, Richard. "snit".