Since the hemipolyhedra have faces passing through the center, the dual figures have corresponding vertices at infinity; properly, on the real projective plane at infinity.[1] In Magnus Wenninger's Dual Models, they are represented with intersecting prisms, each extending in both directions to the same vertex at infinity, in order to maintain symmetry. In practice the model prisms are cut off at a certain point that is convenient for the maker. Wenninger suggested these figures are members of a new class of stellation figures, called stellation to infinity. However, he also suggested that strictly speaking they are not polyhedra because their construction does not conform to the usual definitions.
Since the small dodecahemicosahedron has ten hexagonalfaces passing through the model center, it can be seen as having ten vertices at infinity.
See alsoedit
Hemi-icosahedron - The ten vertices at infinity correspond directionally to the 10 vertices of this abstract polyhedron.
small, dodecahemicosacron, type, star, polyhedronface, elements, symmetry, group, 532index, references, du62dual, polyhedron, small, dodecahemicosahedronin, geometry, small, dodecahemicosacron, dual, small, dodecahemicosahedron, nine, dual, hemipolyhedra, appe. Small dodecahemicosacronType Star polyhedronFace Elements F 30 E 60V 22 x 8 Symmetry group Ih 5 3 532Index references DU62dual polyhedron Small dodecahemicosahedronIn geometry the small dodecahemicosacron is the dual of the small dodecahemicosahedron and is one of nine dual hemipolyhedra It appears visually indistinct from the great dodecahemicosacron Since the hemipolyhedra have faces passing through the center the dual figures have corresponding vertices at infinity properly on the real projective plane at infinity 1 In Magnus Wenninger s Dual Models they are represented with intersecting prisms each extending in both directions to the same vertex at infinity in order to maintain symmetry In practice the model prisms are cut off at a certain point that is convenient for the maker Wenninger suggested these figures are members of a new class of stellation figures called stellation to infinity However he also suggested that strictly speaking they are not polyhedra because their construction does not conform to the usual definitions Since the small dodecahemicosahedron has ten hexagonal faces passing through the model center it can be seen as having ten vertices at infinity See also editHemi icosahedron The ten vertices at infinity correspond directionally to the 10 vertices of this abstract polyhedron References edit Wenninger 2003 p 101 Wenninger Magnus 2003 1983 Dual Models Cambridge University Press doi 10 1017 CBO9780511569371 ISBN 978 0 521 54325 5 MR 0730208 Page 101 Duals of the nine hemipolyhedra External links editWeisstein Eric W Small dodecahemicosacron MathWorld 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 Small dodecahemicosacron amp oldid 1129952285, wikipedia, wiki, book, books, library,
