Overview
- Group
- SmallGroup(1152,98807)
- Rank
- 4
- Schläfli Type
- {2,8,4}
- Vertices, edges, …
- 2, 72, 144, 36
- Order of s0s1s2s3
- 24
- 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)( 6,51)( 7,53)( 8,52)( 9,54)(10,56)(11,55)(12,39)(13,41)(14,40)(15,42)(16,44)(17,43)(18,45)(19,47)(20,46)(21,66)(22,68)(23,67)(24,69)(25,71)(26,70)(27,72)(28,74)(29,73)(30,57)(31,59)(32,58)(33,60)(34,62)(35,61)(36,63)(37,65)(38,64);; 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, 6)( 4, 7)( 5, 8)(12,15)(13,16)(14,17)(21,33)(22,34)(23,35)(24,30)(25,31)(26,32)(27,36)(28,37)(29,38)(39,42)(40,43)(41,44)(48,51)(49,52)(50,53)(57,69)(58,70)(59,71)(60,66)(61,67)(62,68)(63,72)(64,73)(65,74);; 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2,
s1*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(74)!(1,2); s1 := Sym(74)!( 3,48)( 4,50)( 5,49)( 6,51)( 7,53)( 8,52)( 9,54)(10,56)(11,55)(12,39)(13,41)(14,40)(15,42)(16,44)(17,43)(18,45)(19,47)(20,46)(21,66)(22,68)(23,67)(24,69)(25,71)(26,70)(27,72)(28,74)(29,73)(30,57)(31,59)(32,58)(33,60)(34,62)(35,61)(36,63)(37,65)(38,64); 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, 6)( 4, 7)( 5, 8)(12,15)(13,16)(14,17)(21,33)(22,34)(23,35)(24,30)(25,31)(26,32)(27,36)(28,37)(29,38)(39,42)(40,43)(41,44)(48,51)(49,52)(50,53)(57,69)(58,70)(59,71)(60,66)(61,67)(62,68)(63,72)(64,73)(65,74); 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, s1*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1*s2 >;