Pentahexagonal pyritoheptacontatetrahedron
Appearance
Pentahexagonal pyritoheptacontatetrahedron | |
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Type | Near-miss Johnson solid Symmetrohedron |
Faces | 74: 6 hexagons 12 pentagons 8+24+24 non-equilateral triangles |
Edges | 132 |
Vertices | 60 |
Vertex configuration | 3.3.5.6 3.5.3.6 3.3.3.3.5 |
Symmetry group | Th, [3+,4], (3*2), order 24 |
Rotation group | T, [3,3]+, (332), order 12 |
Properties | convex |
Net | |
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![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Pyritohedral_near-miss_johnson-polydron.jpg/220px-Pyritohedral_near-miss_johnson-polydron.jpg)
In geometry, a pentahexagonal pyritoheptacontatetrahedron is a near-miss Johnson solid with pyritohedral symmetry. This near-miss was discovered by Mason Green in 2006. It has 6 hexagonal faces, 12 pentagonal faces, and 56 triangles in 3 symmetry positions. Mason calls it a hexagonally expanded snubbed dodecahedron.[1]
With regular hexagons and pentagons it is a symmetrohedron.[2] The triangles are not equilateral, with triangle-triangle edges compressed by 1.8%.
It has 3 vertex configurations, 3.3.5.6, 3.5.3.6, 3.3.3.3.5, with the last shared in the snub dodecahedron.
See also
[edit]- Tetrated dodecahedron has tetrahedral symmetry
References
[edit]- ^ Near Misses based on dodecahedra
- ^ Kaplan, Craig S.; Hart, George W. (2001), "Symmetrohedra: Polyhedra from Symmetric Placement of Regular Polygons", Bridges: Mathematical Connections in Art, Music and Science (PDF).
External links
[edit]- Near Misses Archived 2012-07-16 at the Wayback Machine
- 24 Johnson Solid Near Misses