Overview
- Group
- SmallGroup(1152,152550)
- Rank
- 5
- Schläfli Type
- {2,2,24,6}
- Vertices, edges, …
- 2, 2, 24, 72, 6
- 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 := ( 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);; 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)(23,71)(24,73)(25,72)(26,68)(27,70)(28,69)(29,74)(30,76)(31,75)(32,62)(33,64)(34,63)(35,59)(36,61)(37,60)(38,65)(39,67)(40,66);; s4 := ( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)(26,30)(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,42)(44,48)(45,47)(46,49)(50,51)(53,57)(54,56)(55,58)(59,60)(62,66)(63,65)(64,67)(68,69)(71,75)(72,74)(73,76);; 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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*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)!( 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); 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)(23,71)(24,73)(25,72)(26,68)(27,70)(28,69)(29,74)(30,76)(31,75)(32,62)(33,64)(34,63)(35,59)(36,61)(37,60)(38,65)(39,67)(40,66); s4 := Sym(76)!( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)(26,30)(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,42)(44,48)(45,47)(46,49)(50,51)(53,57)(54,56)(55,58)(59,60)(62,66)(63,65)(64,67)(68,69)(71,75)(72,74)(73,76); 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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s4*s2*s3, s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3 >;