Overview
- Group
- SmallGroup(1152,157863)
- Rank
- 5
- Schläfli Type
- {2,2,6,6}
- Vertices, edges, …
- 2, 2, 24, 72, 24
- Order of s0s1s2s3s4
- 12
- 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
12-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)(10,11)(14,15)(17,29)(18,31)(19,30)(20,32)(21,33)(22,35)(23,34)(24,36)(25,37)(26,39)(27,38)(28,40)(42,43)(46,47)(50,51)(53,65)(54,67)(55,66)(56,68)(57,69)(58,71)(59,70)(60,72)(61,73)(62,75)(63,74)(64,76);; s3 := ( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)(10,26)(11,28)(12,27)(13,21)(14,22)(15,24)(16,23)(31,32)(33,37)(34,38)(35,40)(36,39)(41,53)(42,54)(43,56)(44,55)(45,61)(46,62)(47,64)(48,63)(49,57)(50,58)(51,60)(52,59)(67,68)(69,73)(70,74)(71,76)(72,75);; s4 := ( 5,48)( 6,46)( 7,47)( 8,45)( 9,44)(10,42)(11,43)(12,41)(13,52)(14,50)(15,51)(16,49)(17,72)(18,70)(19,71)(20,69)(21,68)(22,66)(23,67)(24,65)(25,76)(26,74)(27,75)(28,73)(29,60)(30,58)(31,59)(32,57)(33,56)(34,54)(35,55)(36,53)(37,64)(38,62)(39,63)(40,61);; 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*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(76)!(1,2); s1 := Sym(76)!(3,4); s2 := Sym(76)!( 6, 7)(10,11)(14,15)(17,29)(18,31)(19,30)(20,32)(21,33)(22,35)(23,34)(24,36)(25,37)(26,39)(27,38)(28,40)(42,43)(46,47)(50,51)(53,65)(54,67)(55,66)(56,68)(57,69)(58,71)(59,70)(60,72)(61,73)(62,75)(63,74)(64,76); s3 := Sym(76)!( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)(10,26)(11,28)(12,27)(13,21)(14,22)(15,24)(16,23)(31,32)(33,37)(34,38)(35,40)(36,39)(41,53)(42,54)(43,56)(44,55)(45,61)(46,62)(47,64)(48,63)(49,57)(50,58)(51,60)(52,59)(67,68)(69,73)(70,74)(71,76)(72,75); s4 := Sym(76)!( 5,48)( 6,46)( 7,47)( 8,45)( 9,44)(10,42)(11,43)(12,41)(13,52)(14,50)(15,51)(16,49)(17,72)(18,70)(19,71)(20,69)(21,68)(22,66)(23,67)(24,65)(25,76)(26,74)(27,75)(28,73)(29,60)(30,58)(31,59)(32,57)(33,56)(34,54)(35,55)(36,53)(37,64)(38,62)(39,63)(40,61); 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*s3*s2*s3*s4*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3 >;