Overview
- Group
- SmallGroup(864,2462)
- Rank
- 5
- Schläfli Type
- {3,2,4,18}
- Vertices, edges, …
- 3, 3, 4, 36, 18
- Order of s0s1s2s3s4
- 36
- 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
4-fold
6-fold
9-fold
12-fold
18-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := (22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39);; s3 := ( 4,22)( 5,24)( 6,23)( 7,29)( 8,28)( 9,30)(10,26)(11,25)(12,27)(13,31)(14,33)(15,32)(16,38)(17,37)(18,39)(19,35)(20,34)(21,36);; s4 := ( 4, 7)( 5, 9)( 6, 8)(10,11)(13,16)(14,18)(15,17)(19,20)(22,25)(23,27)(24,26)(28,29)(31,34)(32,36)(33,35)(37,38);; 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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(39)!(2,3); s1 := Sym(39)!(1,2); s2 := Sym(39)!(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39); s3 := Sym(39)!( 4,22)( 5,24)( 6,23)( 7,29)( 8,28)( 9,30)(10,26)(11,25)(12,27)(13,31)(14,33)(15,32)(16,38)(17,37)(18,39)(19,35)(20,34)(21,36); s4 := Sym(39)!( 4, 7)( 5, 9)( 6, 8)(10,11)(13,16)(14,18)(15,17)(19,20)(22,25)(23,27)(24,26)(28,29)(31,34)(32,36)(33,35)(37,38); poly := sub<Sym(39)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;