Final stellation of the cuboctahedron

Final stellation of the cuboctahedron
(OFF file)
Rank	3
Elements
Components	1 semi-uniform quasitruncated hexahedron, 2 tetrahedra
Faces	8+8 triangles as 8 irregular hexagrams, 6 nonconvex ditetragons
Edges	24+12+12
Vertices	24+8
Measures (unit-edge core cuboctahedron)
Edge lengths	24×5
	12×$4{\sqrt {2}}\approx 5.65685$
	12×4
Volume	${\frac {151{\sqrt {2}}}{3}}\approx 71.18208$
Related polytopes
Conjugate	None
Convex core	Cuboctahedron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

The final stellation of the cuboctahedron is a compund polyhedron composed of a semi-uniform quasitruncated hexahedron and a stella octangula, which itself is made of two tetrahedra. Other than being the final stellation of the cuboctahedron, It has no other special properties. It has 8 ditetragrammal faces and 16 triangles of two different sizes, combining into irregular hexagrams.

Vertex coordinates

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

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