Final stellation of the rhombic dodecahedron

Final stellation of the rhombic dodecahedron
(OFF file)
Rank	3
Elements
Faces	12 irregular hexagrams
Edges	12+24
Vertices	24
Vertex figure	Isosceles triangle
Related polytopes
Army	Toe
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

The final stellation of the rhombic dodecahedron is a noble polyhedron compound that is a faceting of the uniform truncated octahedron. It has 24 isosceles triangles as faces in coplanar pairs, forming 12 irregular hexagrams. It is a compound of six tetragonal disphenoids.

Vertex coordinates

The vertices of the final stellation of the rhombic dodecahedron with core edge length 1 are given by all permutations of:

• $\left(\pm {\frac {4{\sqrt {3}}}{3}},\,\pm {\frac {2{\sqrt {3}}}{3}},\,0\right).$