Pentagrammic crossed-antiprism





















































Uniform Pentagrammic crossed-antiprism

Pentagrammic crossed antiprism.png
Type
Prismatic uniform polyhedron
Elements
F = 12, E = 20
V = 10 (χ = 2)
Faces by sides 10{3}+2{5/2}
Schläfli symbol s{2,10/3}
sr{2,5/3}
Wythoff symbol | 2 2 5/3
Coxeter diagram
CDel node h.pngCDel 2x.pngCDel node h.pngCDel 10.pngCDel rat.pngCDel d3.pngCDel node.png
=CDel node h.pngCDel 2x.pngCDel node h.pngCDel 5.pngCDel rat.pngCDel d3.pngCDel node h.png
Symmetry
D5h, [5,2], (*522), order 20
Rotation group D5, [5,2]+, (552), order 10
D5d
Index references
U80(a)
Dual
Pentagrammic concave trapezohedron
Properties
nonconvex

Pentagrammic crossed-antiprism vertfig.png
Vertex figure
3.3.3.5/3 or 3.3.3.-5/2

In geometry, the pentagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.


It differs from the pentagrammic antiprism by having opposite orientations on the two pentagrams.


This polyhedron is identified with the indexed name U80 as a uniform polyhedron.



Pentagrammic crossed-antiprism.png
An alternative representation with hollow pentagrams.

The pentagrammic crossed-antiprism may be inscribed within an icosahedron, and has ten triangular faces in common with the great icosahedron. It has the same vertex arrangement as the pentagonal antiprism. In fact, it may be considered as a parabidiminished great icosahedron.






Pentagrammic crossed antiprism.png
Pentagrammic crossed-antiprism
Dihedral gike.png
Great icosahedron coloured with D5d symmetry




See also


  • Prismatic uniform polyhedron


External links



  • Weisstein, Eric W. "Pentagrammic crossed antiprism". MathWorld..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"""""""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}

  • http://www.mathconsult.ch/showroom/unipoly/80.html

  • http://bulatov.org/polyhedra/uniform/u05.html

  • https://web.archive.org/web/20050313234519/http://www.math.technion.ac.il/~rl/kaleido/data/05.html








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