Overview
- Group
- SmallGroup(1152,98807)
- Rank
- 4
- Schläfli Type
- {2,4,24}
- Vertices, edges, …
- 2, 12, 144, 72
- 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 := ( 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);; s2 := ( 4, 6)( 5, 9)( 8,10)(13,15)(14,18)(17,19)(21,30)(22,33)(23,36)(24,31)(25,34)(26,37)(27,32)(28,35)(29,38)(39,57)(40,60)(41,63)(42,58)(43,61)(44,64)(45,59)(46,62)(47,65)(48,66)(49,69)(50,72)(51,67)(52,70)(53,73)(54,68)(55,71)(56,74);; s3 := ( 3,49)( 4,48)( 5,50)( 6,55)( 7,54)( 8,56)( 9,52)(10,51)(11,53)(12,40)(13,39)(14,41)(15,46)(16,45)(17,47)(18,43)(19,42)(20,44)(21,58)(22,57)(23,59)(24,64)(25,63)(26,65)(27,61)(28,60)(29,62)(30,67)(31,66)(32,68)(33,73)(34,72)(35,74)(36,70)(37,69)(38,71);; 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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2,
s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(74)!(1,2); s1 := 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); s2 := Sym(74)!( 4, 6)( 5, 9)( 8,10)(13,15)(14,18)(17,19)(21,30)(22,33)(23,36)(24,31)(25,34)(26,37)(27,32)(28,35)(29,38)(39,57)(40,60)(41,63)(42,58)(43,61)(44,64)(45,59)(46,62)(47,65)(48,66)(49,69)(50,72)(51,67)(52,70)(53,73)(54,68)(55,71)(56,74); s3 := Sym(74)!( 3,49)( 4,48)( 5,50)( 6,55)( 7,54)( 8,56)( 9,52)(10,51)(11,53)(12,40)(13,39)(14,41)(15,46)(16,45)(17,47)(18,43)(19,42)(20,44)(21,58)(22,57)(23,59)(24,64)(25,63)(26,65)(27,61)(28,60)(29,62)(30,67)(31,66)(32,68)(33,73)(34,72)(35,74)(36,70)(37,69)(38,71); 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, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2, s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2, s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1 >;