Overview
- Group
- SmallGroup(1152,134258)
- Rank
- 5
- Schläfli Type
- {2,2,36,4}
- Vertices, edges, …
- 2, 2, 36, 72, 4
- Order of s0s1s2s3s4
- 36
- 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)( 8,12)( 9,11)(10,13)(15,16)(17,21)(18,20)(19,22)(24,25)(26,30)(27,29)(28,31)(33,34)(35,39)(36,38)(37,40)(41,59)(42,61)(43,60)(44,66)(45,65)(46,67)(47,63)(48,62)(49,64)(50,68)(51,70)(52,69)(53,75)(54,74)(55,76)(56,72)(57,71)(58,73);; s3 := ( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,48)(12,47)(13,49)(14,53)(15,55)(16,54)(17,50)(18,52)(19,51)(20,57)(21,56)(22,58)(23,62)(24,64)(25,63)(26,59)(27,61)(28,60)(29,66)(30,65)(31,67)(32,71)(33,73)(34,72)(35,68)(36,70)(37,69)(38,75)(39,74)(40,76);; s4 := (41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(48,57)(49,58)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74)(66,75)(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,
s3*s4*s3*s4*s3*s4*s3*s4, s2*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*s2*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(76)!(1,2); s1 := Sym(76)!(3,4); s2 := Sym(76)!( 6, 7)( 8,12)( 9,11)(10,13)(15,16)(17,21)(18,20)(19,22)(24,25)(26,30)(27,29)(28,31)(33,34)(35,39)(36,38)(37,40)(41,59)(42,61)(43,60)(44,66)(45,65)(46,67)(47,63)(48,62)(49,64)(50,68)(51,70)(52,69)(53,75)(54,74)(55,76)(56,72)(57,71)(58,73); s3 := Sym(76)!( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,48)(12,47)(13,49)(14,53)(15,55)(16,54)(17,50)(18,52)(19,51)(20,57)(21,56)(22,58)(23,62)(24,64)(25,63)(26,59)(27,61)(28,60)(29,66)(30,65)(31,67)(32,71)(33,73)(34,72)(35,68)(36,70)(37,69)(38,75)(39,74)(40,76); s4 := Sym(76)!(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(48,57)(49,58)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74)(66,75)(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, s3*s4*s3*s4*s3*s4*s3*s4, s2*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*s2*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;