Sesquitruncated octahedron

Sesquitruncated octahedron
(OFF file)
Rank	3
Type	Near-miss
Space	Spherical
Elements
Faces	24 isosceles triangles, 6 squares, 8 triangular-symmetric enneagons
Edges	12+24+48
Vertices	24+24
Vertex figures	24 isosceles triangles
	24 isosceles trapezoids
Measures (based on regular enneagons of edge length 1)
Edge length ratio	$\sqrt{\frac{4-4\cos\frac\pi9+4\cos\frac{2\pi}{9}}{3}} \approx 1.04967$
Circumradius	$\sqrt{\frac{5+4\cos\frac\pi9+4\cos\frac{2\pi}{9}}{2}} \approx 2.43135$
Central density	1
Number of external pieces	38
Related polytopes
Conjugate	None
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	B3, order 48
Convex	Yes
Nature	Tame

The sesquitruncated octahedron is a near-miss Johnson solid. Its faces are 24 isosceles triangles, 6 squares and 8 enneagons.

To construct it, one needs to inscribe an enneagon in every face of a regular octahedron and fill all the remaining gaps with triangles and squares.

The sesquitruncated octahedron is a cell of the sesquitruncated rectified cubic honeycomb which is a near-miss CRF honeycomb.

Its other cell types are: sesquitruncated cuboctahedra, deformed cuboctahedra and deformed tetrahedra.

Variations

There is one variant of the sesquitruncated octahedron with regular enneagons. If the edge length of the enneagon is 1, the other edge length is $\sqrt{\frac{4-4\cos\frac\pi9+4\cos\frac{2\pi}{9}}{3}}$ ≈ 1.04967.

Net

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