Overview
- Group
- SmallGroup(1152,98807)
- Rank
- 4
- Schläfli Type
- {2,24,4}
- Vertices, edges, …
- 2, 72, 144, 12
- Order of s0s1s2s3
- 8
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
9-fold
18-fold
36-fold
72-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,48)( 4,50)( 5,49)( 6,54)( 7,56)( 8,55)( 9,51)(10,53)(11,52)(12,39)(13,41)(14,40)(15,45)(16,47)(17,46)(18,42)(19,44)(20,43)(21,57)(22,59)(23,58)(24,63)(25,65)(26,64)(27,60)(28,62)(29,61)(30,66)(31,68)(32,67)(33,72)(34,74)(35,73)(36,69)(37,71)(38,70);; s2 := ( 3, 7)( 5,10)( 8, 9)(12,16)(14,19)(17,18)(21,34)(22,31)(23,37)(24,33)(25,30)(26,36)(27,35)(28,32)(29,38)(39,70)(40,67)(41,73)(42,69)(43,66)(44,72)(45,71)(46,68)(47,74)(48,61)(49,58)(50,64)(51,60)(52,57)(53,63)(54,62)(55,59)(56,65);; s3 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)(24,36)(25,37)(26,38)(27,33)(28,34)(29,35)(42,45)(43,46)(44,47)(51,54)(52,55)(53,56)(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71);; 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*s2*s3*s2*s3, s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(74)!(1,2); s1 := Sym(74)!( 3,48)( 4,50)( 5,49)( 6,54)( 7,56)( 8,55)( 9,51)(10,53)(11,52)(12,39)(13,41)(14,40)(15,45)(16,47)(17,46)(18,42)(19,44)(20,43)(21,57)(22,59)(23,58)(24,63)(25,65)(26,64)(27,60)(28,62)(29,61)(30,66)(31,68)(32,67)(33,72)(34,74)(35,73)(36,69)(37,71)(38,70); s2 := Sym(74)!( 3, 7)( 5,10)( 8, 9)(12,16)(14,19)(17,18)(21,34)(22,31)(23,37)(24,33)(25,30)(26,36)(27,35)(28,32)(29,38)(39,70)(40,67)(41,73)(42,69)(43,66)(44,72)(45,71)(46,68)(47,74)(48,61)(49,58)(50,64)(51,60)(52,57)(53,63)(54,62)(55,59)(56,65); s3 := Sym(74)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)(24,36)(25,37)(26,38)(27,33)(28,34)(29,35)(42,45)(43,46)(44,47)(51,54)(52,55)(53,56)(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71); poly := sub<Sym(74)|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*s2*s3*s2*s3, s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2, s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2 >;