Overview
- Group
- SmallGroup(192,1542)
- Rank
- 6
- Schläfli Type
- {2,2,2,2,6}
- Vertices, edges, …
- 2, 2, 2, 2, 6, 6
- Order of s0s1s2s3s4s5
- 6
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
- {2,2,4,4,6}*768
- {2,4,4,2,6}*768
- {4,4,2,2,6}*768
- {2,2,2,4,12}*768a
- {2,4,2,4,6}*768a
- {4,2,2,4,6}*768a
- {4,2,4,2,6}*768
- {2,2,4,2,12}*768
- {2,4,2,2,12}*768
- {4,2,2,2,12}*768
- {2,2,2,8,6}*768
- {2,2,8,2,6}*768
- {2,8,2,2,6}*768
- {8,2,2,2,6}*768
- {2,2,2,2,24}*768
- {2,2,2,4,6}*768
5-fold
6-fold
- {2,2,2,4,18}*1152a
- {2,2,4,2,18}*1152
- {2,4,2,2,18}*1152
- {4,2,2,2,18}*1152
- {2,2,2,2,36}*1152
- {2,2,4,6,6}*1152a
- {2,2,6,4,6}*1152
- {2,4,2,6,6}*1152a
- {2,4,2,6,6}*1152b
- {2,4,6,2,6}*1152a
- {2,6,2,4,6}*1152a
- {2,6,4,2,6}*1152a
- {4,2,2,6,6}*1152a
- {4,2,2,6,6}*1152b
- {4,2,6,2,6}*1152
- {4,6,2,2,6}*1152a
- {6,2,2,4,6}*1152a
- {6,2,4,2,6}*1152
- {6,4,2,2,6}*1152a
- {2,2,2,12,6}*1152a
- {2,2,4,6,6}*1152c
- {2,2,2,6,12}*1152b
- {2,2,2,6,12}*1152c
- {2,2,2,12,6}*1152b
- {2,2,6,2,12}*1152
- {2,2,12,2,6}*1152
- {2,6,2,2,12}*1152
- {2,12,2,2,6}*1152
- {6,2,2,2,12}*1152
- {12,2,2,2,6}*1152
7-fold
9-fold
- {2,2,2,2,54}*1728
- {2,2,2,6,18}*1728a
- {2,2,2,6,18}*1728b
- {2,2,2,18,6}*1728a
- {2,2,6,2,18}*1728
- {2,2,18,2,6}*1728
- {2,6,2,2,18}*1728
- {2,18,2,2,6}*1728
- {6,2,2,2,18}*1728
- {18,2,2,2,6}*1728
- {2,2,2,6,6}*1728a
- {2,2,2,6,6}*1728b
- {2,2,6,6,6}*1728a
- {2,2,2,6,6}*1728d
- {2,2,6,6,6}*1728b
- {2,2,6,6,6}*1728c
- {2,2,6,6,6}*1728d
- {2,2,6,6,6}*1728g
- {2,6,2,6,6}*1728a
- {2,6,2,6,6}*1728b
- {2,6,6,2,6}*1728a
- {2,6,6,2,6}*1728b
- {2,6,6,2,6}*1728c
- {6,2,2,6,6}*1728a
- {6,2,2,6,6}*1728b
- {6,2,6,2,6}*1728
- {6,6,2,2,6}*1728a
- {6,6,2,2,6}*1728b
- {6,6,2,2,6}*1728c
10-fold
- {2,2,2,4,30}*1920a
- {2,2,4,2,30}*1920
- {2,4,2,2,30}*1920
- {4,2,2,2,30}*1920
- {2,2,2,2,60}*1920
- {2,2,4,10,6}*1920
- {2,2,10,4,6}*1920
- {2,4,2,10,6}*1920
- {2,4,10,2,6}*1920
- {2,10,2,4,6}*1920a
- {2,10,4,2,6}*1920
- {4,2,2,10,6}*1920
- {4,2,10,2,6}*1920
- {4,10,2,2,6}*1920
- {10,2,2,4,6}*1920a
- {10,2,4,2,6}*1920
- {10,4,2,2,6}*1920
- {2,2,2,10,12}*1920
- {2,2,10,2,12}*1920
- {2,10,2,2,12}*1920
- {10,2,2,2,12}*1920
- {2,2,2,20,6}*1920a
- {2,2,20,2,6}*1920
- {2,20,2,2,6}*1920
- {20,2,2,2,6}*1920
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := (5,6);; s3 := (7,8);; s4 := (11,12)(13,14);; s5 := ( 9,13)(10,11)(12,14);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(14)!(1,2); s1 := Sym(14)!(3,4); s2 := Sym(14)!(5,6); s3 := Sym(14)!(7,8); s4 := Sym(14)!(11,12)(13,14); s5 := Sym(14)!( 9,13)(10,11)(12,14); poly := sub<Sym(14)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;