Overview
- Group
- SmallGroup(1152,134272)
- Rank
- 5
- Schläfli Type
- {2,2,12,12}
- Vertices, edges, …
- 2, 2, 12, 72, 12
- 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
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 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)(35,38)(36,39)(37,40)(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);; s3 := ( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)(14,53)(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,62)(24,64)(25,63)(26,59)(27,61)(28,60)(29,65)(30,67)(31,66)(32,71)(33,73)(34,72)(35,68)(36,70)(37,69)(38,74)(39,76)(40,75);; s4 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,51)(42,50)(43,52)(44,54)(45,53)(46,55)(47,57)(48,56)(49,58)(59,69)(60,68)(61,70)(62,72)(63,71)(64,73)(65,75)(66,74)(67,76);; 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*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(76)!(1,2); s1 := Sym(76)!(3,4); s2 := Sym(76)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)(35,38)(36,39)(37,40)(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); s3 := Sym(76)!( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)(14,53)(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,62)(24,64)(25,63)(26,59)(27,61)(28,60)(29,65)(30,67)(31,66)(32,71)(33,73)(34,72)(35,68)(36,70)(37,69)(38,74)(39,76)(40,75); s4 := Sym(76)!( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,51)(42,50)(43,52)(44,54)(45,53)(46,55)(47,57)(48,56)(49,58)(59,69)(60,68)(61,70)(62,72)(63,71)(64,73)(65,75)(66,74)(67,76); 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*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;