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[[File:Small icosihemidodecahedron.stl|thumb|3D model of a small icosihemidodecahedron]]
[[File:Small icosihemidodecahedron.stl|thumb|3D model of a small icosihemidodecahedron]]


In [[geometry]], the '''small icosihemidodecahedron''' (or '''small icosahemidodecahedron''') is a [[uniform star polyhedron]], indexed as {{math|U{{sub|49}}}}. It has 26 faces (20 [[Triangle|triangles]] and 6 [[Decagon|decagons]]), 60 [[Edge (geometry)|edges]], and 30 [[Vertex (geometry)|vertices]].<ref>{{Cite web|url=https://www.mathconsult.ch/enwiki/static/unipoly/49.html|title=49: small icosihemidodecahedron|last=Maeder|first=Roman|date=|website=MathConsult|url-status=live|archive-url=|archive-date=|access-date=}}</ref> Its [[vertex figure]] alternates two regular triangles and [[decagon]]s as a [[antiparallelogram|crossed quadrilateral]]. It is a [[hemipolyhedron]] with its six decagonal faces passing through the model center.
In [[geometry]], the '''small icosihemidodecahedron''' (or '''small icosahemidodecahedron''') is a [[uniform star polyhedron]], indexed as {{math|U{{sub|49}}}}. It has 26 faces (20 [[Triangle|triangles]] and 6 [[Decagon|decagons]]), 60 [[Edge (geometry)|edges]], and 30 [[Vertex (geometry)|vertices]].<ref>{{Cite web|url=https://www.mathconsult.ch/enwiki/static/unipoly/49.html|title=49: small icosihemidodecahedron|last=Maeder|first=Roman|date=|website=MathConsult|archive-url=|archive-date=|access-date=}}</ref> Its [[vertex figure]] alternates two regular triangles and [[decagon]]s as a [[antiparallelogram|crossed quadrilateral]]. It is a [[hemipolyhedron]] with its six decagonal faces passing through the model center.


It is given a [[Wythoff symbol]], {{math|{{frac|3|2}} 3 {{!}} 5,}} but that construction represents a double covering of this model.
It is given a [[Wythoff symbol]], {{math|{{frac|3|2}} 3 {{!}} 5,}} but that construction represents a double covering of this model.

Latest revision as of 11:28, 27 September 2023

Small icosihemidodecahedron
Type Uniform star polyhedron
Elements F = 26, E = 60
V = 30 (χ = −4)
Faces by sides 20{3}+6{10}
Coxeter diagram (double covering)
Wythoff symbol 3/2 3 | 5 (double covering)
Symmetry group Ih, [5,3], *532
Index references U49, C63, W89
Dual polyhedron Small icosihemidodecacron
Vertex figure
3.10.3/2.10
Bowers acronym Seihid
3D model of a small icosihemidodecahedron

In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as U49. It has 26 faces (20 triangles and 6 decagons), 60 edges, and 30 vertices.[1] Its vertex figure alternates two regular triangles and decagons as a crossed quadrilateral. It is a hemipolyhedron with its six decagonal faces passing through the model center.

It is given a Wythoff symbol, 32 3 | 5, but that construction represents a double covering of this model.

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It shares its edge arrangement with the icosidodecahedron (its convex hull, having the triangular faces in common), and with the small dodecahemidodecahedron (having the decagonal faces in common).


Icosidodecahedron

Small icosihemidodecahedron

Small dodecahemidodecahedron

See also

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References

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  1. ^ Maeder, Roman. "49: small icosihemidodecahedron". MathConsult.
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