Overview
- Group
- SmallGroup(1920,240798)
- Rank
- 4
- Schläfli Type
- {4,8,5}
- Vertices, edges, …
- 4, 96, 120, 30
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 1,45)( 2,46)( 3,48)( 4,47)( 5,55)( 6,56)( 7,61)( 8,62)( 9,65)(10,66)(11,50)(12,49)(13,69)(14,70)(15,73)(16,74)(17,52)(18,51)(19,77)(20,78)(21,54)(22,53)(23,79)(24,80)(25,58)(26,57)(27,85)(28,86)(29,60)(30,59)(31,82)(32,81)(33,64)(34,63)(35,68)(36,67)(37,75)(38,76)(39,87)(40,88)(41,72)(42,71)(43,84)(44,83);; s1 := ( 1, 3)( 2, 4)( 7,39)( 8,40)( 9,35)(10,36)(11,12)(13,32)(14,31)(15,29)(16,30)(17,44)(18,43)(19,34)(20,33)(21,23)(22,24)(25,38)(26,37)(27,41)(28,42)(45,47)(46,48)(49,50)(51,84)(52,83)(53,80)(54,79)(57,75)(58,76)(59,74)(60,73)(61,87)(62,88)(63,77)(64,78)(65,68)(66,67)(69,81)(70,82)(71,86)(72,85);; s2 := ( 1,45)( 2,46)( 3,47)( 4,48)( 5,59)( 6,60)( 7,61)( 8,62)( 9,83)(10,84)(11,73)(12,74)(13,86)(14,85)(15,50)(16,49)(17,52)(18,51)(19,76)(20,75)(21,87)(22,88)(23,80)(24,79)(25,71)(26,72)(27,70)(28,69)(29,56)(30,55)(31,63)(32,64)(33,81)(34,82)(35,67)(36,68)(37,78)(38,77)(39,54)(40,53)(41,57)(42,58)(43,66)(44,65);; s3 := ( 1,45)( 2,46)( 3,47)( 4,48)( 5,55)( 6,56)( 7,81)( 8,82)( 9,67)(10,68)(11,50)(12,49)(13,87)(14,88)(15,63)(16,64)(17,75)(18,76)(19,60)(20,59)(21,79)(22,80)(23,54)(24,53)(25,84)(26,83)(27,86)(28,85)(29,77)(30,78)(31,62)(32,61)(33,74)(34,73)(35,66)(36,65)(37,52)(38,51)(39,69)(40,70)(41,71)(42,72)(43,58)(44,57);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(88)!( 1,45)( 2,46)( 3,48)( 4,47)( 5,55)( 6,56)( 7,61)( 8,62)( 9,65)(10,66)(11,50)(12,49)(13,69)(14,70)(15,73)(16,74)(17,52)(18,51)(19,77)(20,78)(21,54)(22,53)(23,79)(24,80)(25,58)(26,57)(27,85)(28,86)(29,60)(30,59)(31,82)(32,81)(33,64)(34,63)(35,68)(36,67)(37,75)(38,76)(39,87)(40,88)(41,72)(42,71)(43,84)(44,83); s1 := Sym(88)!( 1, 3)( 2, 4)( 7,39)( 8,40)( 9,35)(10,36)(11,12)(13,32)(14,31)(15,29)(16,30)(17,44)(18,43)(19,34)(20,33)(21,23)(22,24)(25,38)(26,37)(27,41)(28,42)(45,47)(46,48)(49,50)(51,84)(52,83)(53,80)(54,79)(57,75)(58,76)(59,74)(60,73)(61,87)(62,88)(63,77)(64,78)(65,68)(66,67)(69,81)(70,82)(71,86)(72,85); s2 := Sym(88)!( 1,45)( 2,46)( 3,47)( 4,48)( 5,59)( 6,60)( 7,61)( 8,62)( 9,83)(10,84)(11,73)(12,74)(13,86)(14,85)(15,50)(16,49)(17,52)(18,51)(19,76)(20,75)(21,87)(22,88)(23,80)(24,79)(25,71)(26,72)(27,70)(28,69)(29,56)(30,55)(31,63)(32,64)(33,81)(34,82)(35,67)(36,68)(37,78)(38,77)(39,54)(40,53)(41,57)(42,58)(43,66)(44,65); s3 := Sym(88)!( 1,45)( 2,46)( 3,47)( 4,48)( 5,55)( 6,56)( 7,81)( 8,82)( 9,67)(10,68)(11,50)(12,49)(13,87)(14,88)(15,63)(16,64)(17,75)(18,76)(19,60)(20,59)(21,79)(22,80)(23,54)(24,53)(25,84)(26,83)(27,86)(28,85)(29,77)(30,78)(31,62)(32,61)(33,74)(34,73)(35,66)(36,65)(37,52)(38,51)(39,69)(40,70)(41,71)(42,72)(43,58)(44,57); poly := sub<Sym(88)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;
References
None.
to this polytope.