augmented truncated cube
{{Short description|66th Johnson solid}}
{{Infobox polyhedron
|image=augmented_truncated_cube.png
|type=Johnson
{{math|J65 – J66 – J67}}
|faces=3x4 triangles
1+4 squares
1+4 octagons
|edges=48
|vertices=28
|symmetry={{math|C4v}}
|vertex_config={{math|2.4+8(3.82)
4(3.43)
8(3.4.3.8)}}
|dual=-
|properties=convex
|net=Johnson solid 66 net.png
}}
In geometry, the augmented truncated cube is one of the Johnson solids ({{math|J66}}). As its name suggests, it is created by attaching a square cupola ({{math|J4}}) onto one octagonal face of a truncated cube.
{{Johnson solid}}
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.
- {{cite book|author=Victor A. Zalgaller|author-link=Victor Zalgaller|title=Convex Polyhedra with Regular Faces|publisher=Consultants Bureau|year=1969|id=No ISBN}} The first proof that there are only 92 Johnson solids.
External links
- {{Mathworld2 | urlname2 = JohnsonSolid | title2 = Johnson solid | urlname =AugmentedTruncatedCube| title = Augmented truncated cube}}
{{Johnson solids navigator}}
{{Polyhedron-stub}}