# Sesquitruncated octahedron

Sesquitruncated octahedron
Rank3
TypeNear-miss
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${\displaystyle {\sqrt {\frac {4-4\cos {\frac {\pi }{9}}+4\cos {\frac {2\pi }{9}}}{3}}}\approx 1.04967}$
Circumradius${\displaystyle {\sqrt {\frac {5+4\cos {\frac {\pi }{9}}+4\cos {\frac {2\pi }{9}}}{2}}}\approx 2.43135}$
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 ${\displaystyle {\sqrt {\frac {4-4\cos {\frac {\pi }{9}}+4\cos {\frac {2\pi }{9}}}{3}}}}$ ≈ 1.04967.