| Pentakis snub dodecahedron | |
|---|---|
 | |
| Geodesic polyhedron | {3,5+}2,1 |
| Conway | k5sD or dwdI |
| Faces | 140 triangles (3 different kinds: 20 equilateral, 60 isosceles, 60 scalene) |
| Edges | 210 (4 different kinds) |
| Vertices | 72 (2 different kinds: 12 of valence 5 and 60 of valence 6) |
| Vertex configurations | (12) 35 (60) 36 |
| Symmetry group | Icosahedral (I) |
| Dual polyhedron | Order-5 truncated pentagonal hexecontahedron |
| Properties | convex, chiral |
| Net |  (click to enlarge) |
The pentakis snub dodecahedron is a convex polyhedron with 140 triangular faces, 210 edges, and 72 vertices. It has chiral icosahedral symmetry.[1]
Construction
It comes from a topological construction from the snub dodecahedron with the kis operator applied to the pentagonal faces. In this construction, all the faces are computed to be the same distance from the center. 80 of the triangles are equilateral, and 60 triangles from the pentagons are isosceles. It is a (2,1) geodesic polyhedron, made of all triangles. The path between the valence-5 vertices is two edges in a row, and then a turn and one more edge.
See also
- Tetrakis snub cube k4sC
References
- ↑ Spherical Models, IV. Geodesic domes, p.83 Photo 36,{3,5+}2,1
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5
- Chapter 21: Naming the Archimedean and Catalan polyhedra and Tilings (p 284)
- Wenninger, Magnus (1979), Spherical Models, Cambridge University Press, ISBN 978-0-521-29432-4, MR 0552023 Dover 1999 ISBN 978-0-486-40921-4
External links
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