Augmented truncated cube

Augmented truncated cube
Type	Johnson J65 – J66 – J67
Faces	3×4 triangles 1+4 squares 1+4 octagons
Edges	48
Vertices	28
Vertex configuration	2.4+8(3.82) 4(3.43) 8(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 are composed of regular polygon faces but are not uniform polyhedra (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]

3D model of an augmented truncated cube

References

1. Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics , 18: 169–200, doi: 10.4153/cjm-1966-021-8 , MR   0185507, Zbl   0132.14603 .

• Victor A. Zalgaller (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. No ISBN. The first proof that there are only 92 Johnson solids.

External links

• Weisstein, Eric W., "Augmented truncated cube" ("Johnson solid") at MathWorld .