- Source: Great icosihemidodecacron
In geometry, the great icosihemidodecacron is the dual of the great icosihemidodecahedron, and is one of nine dual hemipolyhedra. It appears indistinct from the great dodecahemidodecacron.
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. 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.
The great icosihemidodecacron can be seen as having six vertices at infinity.
See also
Hemi-dodecahedron - The six vertices at infinity correspond directionally to the six vertices of this abstract polyhedron.
References
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
Weisstein, Eric W. "Great icosihemidodecacron". MathWorld.
Kata Kunci Pencarian:
- Daftar bentuk matematika
- Great icosihemidodecacron
- List of mathematical shapes
- Table of polyhedron dihedral angles
- List of polygons, polyhedra and polytopes
- Great icosihemidodecahedron
- Hemipolyhedron
- Great dodecahemidodecacron
- List of isotoxal polyhedra and tilings
- List of Wenninger polyhedron models
