| 释义 |
- Construction
- See also
- References
- External links
| Pentakis snub dodecahedron | | | Geodesic polyhedron | {3,5+}2,1 | | Conway | k5sD or [https://levskaya.github.io/polyhedronisme/?recipe=A10dwdI 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] ConstructionIts name comes from a topological construction from the snub dodecahedron with the kis operator applied to the pentagonal faces. In this construction, all the vertices are computed to be the same distance from the center. The 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 [https://levskaya.github.io/polyhedronisme/?recipe=k4sC&palette=%23ffffff k4sC]
References 1. ^ Spherical Models, IV. Geodesic domes, p.83 Photo 36,{3,5+}2,1
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, {{isbn|978-1-56881-220-5}}
- Chapter 21: Naming the Archimedean and Catalan polyhedra and Tilings (p 284)
- {{Citation|last1=Wenninger |first1=Magnus |author1-link=Magnus Wenninger |title=Spherical Models |publisher=Cambridge University Press |isbn=978-0-521-29432-4 |mr=552023 |year=1979 }} Dover 1999 {{isbn|978-0-486-40921-4}}
External links - Pentakis snub dodecahedron
- VTML polyhedral generator Try "k5sD" (Conway polyhedron notation)
{{polyhedron-stub}} 2 : Geodesic polyhedra|Snub tilings |