Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of antiprisms sharing a common axis of rotational symmetry. It arises from superimposing two copies of the corresponding prismatic compound of antiprisms (without rotational freedom), and rotating each copy by an equal and opposite angle.
This infinite family can be enumerated as follows:
For each positive integer n>0 and for each rational number p/q>3/2 (expressed with p and qcoprime), there occurs the compound of 2np/q-gonal antiprisms (with rotational freedom), with symmetry group:
Dnpd if nq is odd
Dnph if nq is even
Where p/q=2 the component is a tetrahedron, sometimes not considered a true antiprism.
Referencesedit
Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.
This polyhedron-related article is a stub. You can help Wikipedia by expanding it.
prismatic, compound, antiprisms, with, rotational, freedom, compound, gonal, antiprisms, type, uniform, compoundindex, uc22, even, uc24polyhedra, gonal, antiprismsfaces, unless, trianglesedges, 8npvertices, 4npsymmetry, group, fold, antiprismatic, dnpd, even, . Compound of 2n p q gonal antiprisms n 2 p 3 q 1 n 1 p 7 q 2 Type Uniform compoundIndex q odd UC22 q even UC24Polyhedra 2n p q gonal antiprismsFaces 4n p q unless p q 2 4np trianglesEdges 8npVertices 4npSymmetry group nq odd np fold antiprismatic Dnpd nq even np fold prismatic Dnph Subgroup restricting to one constituent q odd 2p fold improper rotation S2p q even p fold rotation Cph Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of antiprisms sharing a common axis of rotational symmetry It arises from superimposing two copies of the corresponding prismatic compound of antiprisms without rotational freedom and rotating each copy by an equal and opposite angle This infinite family can be enumerated as follows For each positive integer n gt 0 and for each rational number p q gt 3 2 expressed with p and q coprime there occurs the compound of 2n p q gonal antiprisms with rotational freedom with symmetry group Dnpd if nq is odd Dnph if nq is evenWhere p q 2 the component is a tetrahedron sometimes not considered a true antiprism References editSkilling John 1976 Uniform Compounds of Uniform Polyhedra Mathematical Proceedings of the Cambridge Philosophical Society 79 3 447 457 doi 10 1017 S0305004100052440 MR 0397554 nbsp This polyhedron related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Prismatic compound of antiprisms with rotational freedom amp oldid 1088011031, wikipedia, wiki, book, books, library,
