Overview
- Group
- SmallGroup(1008,922)
- Rank
- 5
- Schläfli Type
- {3,2,14,6}
- Vertices, edges, …
- 3, 3, 14, 42, 6
- Order of s0s1s2s3s4
- 42
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
6-fold
7-fold
14-fold
21-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 5,10)( 6, 9)( 7, 8)(12,17)(13,16)(14,15)(19,24)(20,23)(21,22)(26,31)(27,30)(28,29)(33,38)(34,37)(35,36)(40,45)(41,44)(42,43)(47,52)(48,51)(49,50)(54,59)(55,58)(56,57)(61,66)(62,65)(63,64)(68,73)(69,72)(70,71)(75,80)(76,79)(77,78)(82,87)(83,86)(84,85);; s3 := ( 4,47)( 5,46)( 6,52)( 7,51)( 8,50)( 9,49)(10,48)(11,61)(12,60)(13,66)(14,65)(15,64)(16,63)(17,62)(18,54)(19,53)(20,59)(21,58)(22,57)(23,56)(24,55)(25,68)(26,67)(27,73)(28,72)(29,71)(30,70)(31,69)(32,82)(33,81)(34,87)(35,86)(36,85)(37,84)(38,83)(39,75)(40,74)(41,80)(42,79)(43,78)(44,77)(45,76);; s4 := ( 4,74)( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,80)(11,67)(12,68)(13,69)(14,70)(15,71)(16,72)(17,73)(18,81)(19,82)(20,83)(21,84)(22,85)(23,86)(24,87)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65)(45,66);; 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*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,
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(87)!(2,3); s1 := Sym(87)!(1,2); s2 := Sym(87)!( 5,10)( 6, 9)( 7, 8)(12,17)(13,16)(14,15)(19,24)(20,23)(21,22)(26,31)(27,30)(28,29)(33,38)(34,37)(35,36)(40,45)(41,44)(42,43)(47,52)(48,51)(49,50)(54,59)(55,58)(56,57)(61,66)(62,65)(63,64)(68,73)(69,72)(70,71)(75,80)(76,79)(77,78)(82,87)(83,86)(84,85); s3 := Sym(87)!( 4,47)( 5,46)( 6,52)( 7,51)( 8,50)( 9,49)(10,48)(11,61)(12,60)(13,66)(14,65)(15,64)(16,63)(17,62)(18,54)(19,53)(20,59)(21,58)(22,57)(23,56)(24,55)(25,68)(26,67)(27,73)(28,72)(29,71)(30,70)(31,69)(32,82)(33,81)(34,87)(35,86)(36,85)(37,84)(38,83)(39,75)(40,74)(41,80)(42,79)(43,78)(44,77)(45,76); s4 := Sym(87)!( 4,74)( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,80)(11,67)(12,68)(13,69)(14,70)(15,71)(16,72)(17,73)(18,81)(19,82)(20,83)(21,84)(22,85)(23,86)(24,87)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65)(45,66); poly := sub<Sym(87)|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*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, s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*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 >;