# Augmented truncated cube

Augmented truncated cube
Type Johnson
J65 - J66 - J67
Faces 3x4 triangles
1+4 squares
1+4 octagons
Edges 48
Vertices 28
Vertex configuration 2.4+8(3.82)
8(3.43)
16(3.4.3.8)
Symmetry group C4v
Dual polyhedron -
Properties convex
Net

In geometry, the augmented truncated cube is one of the Johnson solids (J66). As its name suggests, it is created by attaching a square cupola (J4) onto one octagonal face of a truncated cube.

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.[1]

## References

• Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
• Victor A. Zalgaller (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. No ISBN. The first proof that there are only 92 Johnson solids.