Overview
- Group
- SmallGroup(1152,152550)
- Rank
- 5
- Schläfli Type
- {2,2,6,24}
- Vertices, edges, …
- 2, 2, 6, 72, 24
- Order of s0s1s2s3s4
- 24
- 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
8-fold
9-fold
12-fold
18-fold
24-fold
36-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := ( 6, 7)( 8,11)( 9,13)(10,12)(15,16)(17,20)(18,22)(19,21)(24,25)(26,29)(27,31)(28,30)(33,34)(35,38)(36,40)(37,39)(42,43)(44,47)(45,49)(46,48)(51,52)(53,56)(54,58)(55,57)(60,61)(62,65)(63,67)(64,66)(69,70)(71,74)(72,76)(73,75);; s3 := ( 5,45)( 6,44)( 7,46)( 8,42)( 9,41)(10,43)(11,48)(12,47)(13,49)(14,54)(15,53)(16,55)(17,51)(18,50)(19,52)(20,57)(21,56)(22,58)(23,72)(24,71)(25,73)(26,69)(27,68)(28,70)(29,75)(30,74)(31,76)(32,63)(33,62)(34,64)(35,60)(36,59)(37,61)(38,66)(39,65)(40,67);; s4 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(23,32)(24,33)(25,34)(26,38)(27,39)(28,40)(29,35)(30,36)(31,37)(41,59)(42,60)(43,61)(44,65)(45,66)(46,67)(47,62)(48,63)(49,64)(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)(57,72)(58,73);; 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*s1*s0*s1,
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s4*s2*s3,
s4*s2*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(76)!(1,2); s1 := Sym(76)!(3,4); s2 := Sym(76)!( 6, 7)( 8,11)( 9,13)(10,12)(15,16)(17,20)(18,22)(19,21)(24,25)(26,29)(27,31)(28,30)(33,34)(35,38)(36,40)(37,39)(42,43)(44,47)(45,49)(46,48)(51,52)(53,56)(54,58)(55,57)(60,61)(62,65)(63,67)(64,66)(69,70)(71,74)(72,76)(73,75); s3 := Sym(76)!( 5,45)( 6,44)( 7,46)( 8,42)( 9,41)(10,43)(11,48)(12,47)(13,49)(14,54)(15,53)(16,55)(17,51)(18,50)(19,52)(20,57)(21,56)(22,58)(23,72)(24,71)(25,73)(26,69)(27,68)(28,70)(29,75)(30,74)(31,76)(32,63)(33,62)(34,64)(35,60)(36,59)(37,61)(38,66)(39,65)(40,67); s4 := Sym(76)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(23,32)(24,33)(25,34)(26,38)(27,39)(28,40)(29,35)(30,36)(31,37)(41,59)(42,60)(43,61)(44,65)(45,66)(46,67)(47,62)(48,63)(49,64)(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)(57,72)(58,73); poly := sub<Sym(76)|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*s1*s0*s1, 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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s4*s2*s3, s4*s2*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3*s4*s3 >;