Elongated square cupola

Elongated square cupola
Type	Johnson J18 - J19 - J20
Faces	4 triangles 1+3.4 squares 1 octagon
Edges	36
Vertices	20
Vertex configuration	8(42.8) 4+8(3.43)
Symmetry group	C4v
Dual polyhedron	-
Properties	convex
Net

In geometry, the elongated square cupola is one of the Johnson solids (J₁₉). As the name suggests, it can be constructed by elongating a square cupola (J₄) by attaching an octagonal prism to its base. The solid can be seen as a rhombicuboctahedron with its "lid" (another square cupola) removed.

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.

The following formulae for volume, surface area and circumradius can be used if all faces are regular, with edge length a:

${\displaystyle V=(3+{\frac {8{\sqrt {2}}}{3}})a^{3}\approx 6.77124...a^{3}}$

...
Wikipedia