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Compound of four cubes

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This is an old revision of this page, as edited by Watchduck (talk | contribs) at 22:45, 20 June 2020 (Moved the "Frodelius 5-cube" here from Compound of five cubes. I think it clarifies the symmetry.). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Compound of four cubes
Type Compound
Convex hull Chamfered cube
Polyhedra 4 cubes
Faces 32 squares
Edges 48
Vertices 8+24
Symmetry group octahedral (Oh)
Subgroup restricting to one constituent 3-fold antiprismatic (D3d)

A compound of four cubes is a face-transitive polyhedron compound that is a symmetric arrangement of four cubes, as trigonal trapezohedrons. It can be constructed by dual of compound of four octahedra. Its surface area is 687/77 square lengths of the edge.[1]

Cartesian coordinates

With added fifth cube

Cartesian coordinates for the vertices of this compound are:

(±3, ±3, ±3)
(±5, ±1, ±1)
(±1, ±5, ±1)
(±1, ±1, ±5)

See also

References