Overview
- Group
- SmallGroup(576,8553)
- Rank
- 5
- Schläfli Type
- {2,4,6,6}
- Vertices, edges, …
- 2, 4, 12, 18, 6
- Order of s0s1s2s3s4
- 12
- Order of s0s1s2s3s4s3s2s1
- 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
6-fold
9-fold
12-fold
18-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38);; s2 := ( 3,21)( 4,22)( 5,23)( 6,27)( 7,28)( 8,29)( 9,24)(10,25)(11,26)(12,30)(13,31)(14,32)(15,36)(16,37)(17,38)(18,33)(19,34)(20,35);; s3 := ( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)(22,26)(23,25)(28,29)(30,33)(31,35)(32,34)(37,38);; s4 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(38)!(1,2); s1 := Sym(38)!(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38); s2 := Sym(38)!( 3,21)( 4,22)( 5,23)( 6,27)( 7,28)( 8,29)( 9,24)(10,25)(11,26)(12,30)(13,31)(14,32)(15,36)(16,37)(17,38)(18,33)(19,34)(20,35); s3 := Sym(38)!( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)(22,26)(23,25)(28,29)(30,33)(31,35)(32,34)(37,38); s4 := Sym(38)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37); poly := sub<Sym(38)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;