“Compound of three square antiprisms”的意思、由来-开放百科全书

词条

Compound of three square antiprisms

释义

Cartesian coordinates
References

Compound of three square antiprisms

Type	Uniform compound
Index	UC₄₂
Polyhedra	3 square antiprisms
Faces	24 triangles, 6 squares
Edges	48
Vertices	24
Symmetry group	chiral octahedral (O)
Subgroup restricting to one constituent	4-fold dihedral (D₄)

This uniform polyhedron compound is a symmetric arrangement of 3 square antiprisms, aligned with the three axes of 4-fold rotational symmetry of a cube.

Cartesian coordinates

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

(±√(√2+1), ±√(√2−1), ±1)

with an even number of minuses in the '±' choices, together with all the odd permutations with an odd number of minuses in the '±' choices.

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}}.

1 : Polyhedral compounds

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