Overview
- Group
- SmallGroup(576,1725)
- Rank
- 4
- Schläfli Type
- {2,72,2}
- Vertices, edges, …
- 2, 72, 72, 2
- Order of s0s1s2s3
- 72
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- 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
24-fold
36-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 6,10)( 7, 9)( 8,11)(13,14)(15,19)(16,18)(17,20)(21,30)(22,32)(23,31)(24,37)(25,36)(26,38)(27,34)(28,33)(29,35)(39,57)(40,59)(41,58)(42,64)(43,63)(44,65)(45,61)(46,60)(47,62)(48,66)(49,68)(50,67)(51,73)(52,72)(53,74)(54,70)(55,69)(56,71);; s2 := ( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,46)(10,45)(11,47)(12,51)(13,53)(14,52)(15,48)(16,50)(17,49)(18,55)(19,54)(20,56)(21,69)(22,71)(23,70)(24,66)(25,68)(26,67)(27,73)(28,72)(29,74)(30,60)(31,62)(32,61)(33,57)(34,59)(35,58)(36,64)(37,63)(38,65);; s3 := (75,76);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(76)!(1,2); s1 := Sym(76)!( 4, 5)( 6,10)( 7, 9)( 8,11)(13,14)(15,19)(16,18)(17,20)(21,30)(22,32)(23,31)(24,37)(25,36)(26,38)(27,34)(28,33)(29,35)(39,57)(40,59)(41,58)(42,64)(43,63)(44,65)(45,61)(46,60)(47,62)(48,66)(49,68)(50,67)(51,73)(52,72)(53,74)(54,70)(55,69)(56,71); s2 := Sym(76)!( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,46)(10,45)(11,47)(12,51)(13,53)(14,52)(15,48)(16,50)(17,49)(18,55)(19,54)(20,56)(21,69)(22,71)(23,70)(24,66)(25,68)(26,67)(27,73)(28,72)(29,74)(30,60)(31,62)(32,61)(33,57)(34,59)(35,58)(36,64)(37,63)(38,65); s3 := Sym(76)!(75,76); poly := sub<Sym(76)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;