Overview
- Group
- SmallGroup(288,958)
- Rank
- 4
- Schläfli Type
- {6,4,6}
- Vertices, edges, …
- 6, 12, 12, 6
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{6,4|2},{4,6|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
- Self-Dual
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
9-fold
12-fold
18-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
- {12,4,12}*1152
- {6,8,12}*1152a
- {12,8,6}*1152a
- {6,4,24}*1152a
- {24,4,6}*1152a
- {6,8,12}*1152b
- {12,8,6}*1152b
- {6,4,24}*1152b
- {24,4,6}*1152b
- {6,4,12}*1152a
- {12,4,6}*1152a
- {6,16,6}*1152
- {6,4,6}*1152a
- {6,4,6}*1152b
5-fold
6-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)(31,34)(32,35)(33,36);; s1 := ( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,31)(20,32)(21,33)(22,28)(23,29)(24,30)(25,34)(26,35)(27,36);; s2 := ( 1,19)( 2,21)( 3,20)( 4,22)( 5,24)( 6,23)( 7,25)( 8,27)( 9,26)(10,28)(11,30)(12,29)(13,31)(14,33)(15,32)(16,34)(17,36)(18,35);; s3 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(36)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)(31,34)(32,35)(33,36); s1 := Sym(36)!( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,31)(20,32)(21,33)(22,28)(23,29)(24,30)(25,34)(26,35)(27,36); s2 := Sym(36)!( 1,19)( 2,21)( 3,20)( 4,22)( 5,24)( 6,23)( 7,25)( 8,27)( 9,26)(10,28)(11,30)(12,29)(13,31)(14,33)(15,32)(16,34)(17,36)(18,35); s3 := Sym(36)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35); poly := sub<Sym(36)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.