Pentahexagonal pyritoheptacontatetrahedron
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]
| Pentahexagonal pyritoheptacontatetrahedron | |
|---|---|
 | |
| Faces | 74: 6 hexagons 12 pentagons 8+24+24 triangles |
| Edges | 132 |
| Vertices | 60 |
| Symmetry group | Th, [3+,4], (3*2), order 24 |
| Rotation group | T, [3,3]+, (332), order 12 |
| Properties | convex |
Model built with polydron
With regular hexagons and pentagons it is a symmetrohedron.[2] The triangle 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.
Net
Net
See also
- Tetrated dodecahedron has tetrahedral symmetry
References
- 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
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