Dodecahedral pentagonal polytopes and Coxeter groups
•
0 likes•199 views
Dodecahedral pentagonal polytopes
![Dodecahedral pentagonal polytopes
n Coxeter group
Petrie polygon
projection
Name
Coxeter diagram
Schläfli symbol
Facets
Elements
Vertices Edges Faces Cells 4-faces
1 [ ]
(order 2)
Line segment
{ }
2 vertices 2
2 [5]
(order 10)
Pentagon
{5}
5 edges 5 5
3 [5,3]
(order 120)
Dodecahedron
{5, 3}
12 pentagons
20 30 12
4 [5,3,3]
(order 14400)
120-cell
{5, 3, 3}
120 dodecahedra
600 1200 720 120](https://image.slidesharecdn.com/dppolytopes-150331095511-conversion-gate01/85/Dodecahedral-pentagonal-polytopes-1-320.jpg)
![5 [5,3,3,3]
(order ∞)
120-cell honeycomb
{5, 3, 3, 3}
∞ 120-cells
∞ ∞ ∞ ∞ ∞](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Recommended
Recommended
More Related Content
Viewers also liked
Viewers also liked (20)
More from Prof. C. Annamalai ,
More from Prof. C. Annamalai , (20)
Recently uploaded
Recently uploaded (20)
Dodecahedral pentagonal polytopes and Coxeter groups
- 1. Dodecahedral pentagonal polytopes n Coxeter group Petrie polygon projection Name Coxeter diagram Schläfli symbol Facets Elements Vertices Edges Faces Cells 4-faces 1 [ ] (order 2) Line segment { } 2 vertices 2 2 [5] (order 10) Pentagon {5} 5 edges 5 5 3 [5,3] (order 120) Dodecahedron {5, 3} 12 pentagons 20 30 12 4 [5,3,3] (order 14400) 120-cell {5, 3, 3} 120 dodecahedra 600 1200 720 120
- 2. 5 [5,3,3,3] (order ∞) 120-cell honeycomb {5, 3, 3, 3} ∞ 120-cells ∞ ∞ ∞ ∞ ∞