Sesquitruncated octahedron

The enneagonal-faced octahedral polyhedron is a near-miss Johnson solid. Topologically, its faces are 24 isosceles triangles, 6 squares and 8 triangular-symmetric 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.



Variations
There is one variant of the enneagonal-faced polyhedron 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.