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词条 Compound of four octahedra
释义

  1. Cartesian coordinates

  2. See also

  3. References

Compound of four octahedra
TypeUniform compound
IndexUC12
Convex hullNonuniform truncated cube
Polyhedra4 octahedra
Faces8+24 triangles
Edges48
Vertices24
Symmetry groupoctahedral (Oh)
Subgroup restricting to one constituent3-fold antiprismatic (D3d)

This uniform polyhedron compound is a symmetric arrangement of 4 octahedra, considered as triangular antiprisms. It can be constructed by superimposing four identical octahedra, and then rotating each by 60 degrees about a separate axis (that passes through the centres of two opposite octahedral faces).

Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the permutations of

(±2, ±1, ±2)

See also

  • Compound of three octahedra
  • Compound of five octahedra
  • Compound of ten octahedra
  • Compound of twenty octahedra

References

  • {{citation|first=John|last=Skilling|title=Uniform Compounds of Uniform Polyhedra|journal=Mathematical Proceedings of the Cambridge Philosophical Society|volume=79|issue=03|pages=447–457|year=1976|doi=10.1017/S0305004100052440|mr=0397554}}.
{{polyhedron-stub}}

1 : Polyhedral compounds

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