# Sesquitruncated octahedron

Sesquitruncated octahedron Rank3
TypeNear-miss
SpaceSpherical
Elements
Faces24 isosceles triangles, 6 squares, 8 triangular-symmetric enneagons
Edges12+24+48
Vertices24+24
Vertex figures24 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 density1
Number of external pieces38
Related polytopes
ConjugateNone
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryB3, order 48
ConvexYes
NatureTame

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.