Small rhombidodecahedron











































Small rhombidodecahedron

Small rhombidodecahedron.png
Type
Uniform star polyhedron
Elements
F = 42, E = 120
V = 60 (χ = −18)
Faces by sides 30{4}+12{10}
Wythoff symbol 2 5 (3/25/2) |
Symmetry group Ih, [5,3], *532
Index references
U39, C46, W74
Dual polyhedron
Small rhombidodecacron
Vertex figure
Small rhombidodecahedron vertfig.png
4.10.4/3.10/9
Bowers acronym Sird

In geometry, the small rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U39. Its vertex figure is a crossed quadrilateral.




Contents






  • 1 Related polyhedra


    • 1.1 Small rhombidodecacron




  • 2 References


  • 3 External links





Related polyhedra


It shares its vertex arrangement with the small stellated truncated dodecahedron and the uniform compounds of 6 or 12 pentagrammic prisms. It additionally shares its edge arrangement with the rhombicosidodecahedron (having the square faces in common), and with the small dodecicosidodecahedron (having the decagonal faces in common).














Small rhombicosidodecahedron.png
Rhombicosidodecahedron

Small dodecicosidodecahedron.png
Small dodecicosidodecahedron

Small rhombidodecahedron.png
Small rhombidodecahedron

Small stellated truncated dodecahedron.png
Small stellated truncated dodecahedron

UC36-6 pentagrammic prisms.png
Compound of six pentagrammic prisms

UC37-12 pentagrammic prisms.png
Compound of twelve pentagrammic prisms






Small rhombidodecacron





























Small rhombidodecacron

DU39 small rhombidodecacron.png
Type
Star polyhedron
Face
DU39 facets.png
Elements
F = 60, E = 120
V = 42 (χ = −18)
Symmetry group Ih, [5,3], *532
Index references
DU39
dual polyhedron
Small rhombidodecahedron

The small rhombidodecacron is a nonconvex isohedral polyhedron. It is the dual of the small rhombidodecahedron. It is visually identical to the Small dodecacronic hexecontahedron. It has 60 intersecting antiparallelogram faces.



References



  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208.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}


External links



  • Weisstein, Eric W. "Small rhombidodecahedron". MathWorld.

  • Weisstein, Eric W. "Small rhombidodecacron". MathWorld.

  • Uniform polyhedra and duals











Popular posts from this blog

Italian cuisine

Bulgarian cuisine

Carrot