Overview
- Group
- SmallGroup(1944,2345)
- Rank
- 5
- Schläfli Type
- {3,2,6,9}
- Vertices, edges, …
- 3, 3, 18, 81, 27
- Order of s0s1s2s3s4
- 18
- 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
9-fold
27-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 7,11)( 8,12)( 9,10)(13,22)(14,23)(15,24)(16,29)(17,30)(18,28)(19,27)(20,25)(21,26)(34,38)(35,39)(36,37)(40,49)(41,50)(42,51)(43,56)(44,57)(45,55)(46,54)(47,52)(48,53)(61,65)(62,66)(63,64)(67,76)(68,77)(69,78)(70,83)(71,84)(72,82)(73,81)(74,79)(75,80);; s3 := ( 4,13)( 5,15)( 6,14)( 7,16)( 8,18)( 9,17)(10,19)(11,21)(12,20)(23,24)(26,27)(29,30)(31,68)(32,67)(33,69)(34,71)(35,70)(36,72)(37,74)(38,73)(39,75)(40,59)(41,58)(42,60)(43,62)(44,61)(45,63)(46,65)(47,64)(48,66)(49,77)(50,76)(51,78)(52,80)(53,79)(54,81)(55,83)(56,82)(57,84);; s4 := ( 4,31)( 5,33)( 6,32)( 7,36)( 8,35)( 9,34)(10,38)(11,37)(12,39)(13,56)(14,55)(15,57)(16,49)(17,51)(18,50)(19,54)(20,53)(21,52)(22,43)(23,45)(24,44)(25,48)(26,47)(27,46)(28,41)(29,40)(30,42)(58,59)(62,63)(64,66)(67,84)(68,83)(69,82)(70,77)(71,76)(72,78)(73,79)(74,81)(75,80);; 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s2*s3*s2*s3*s4*s3*s2*s3*s4*s2*s3*s2*s4*s3*s2*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(84)!(2,3); s1 := Sym(84)!(1,2); s2 := Sym(84)!( 7,11)( 8,12)( 9,10)(13,22)(14,23)(15,24)(16,29)(17,30)(18,28)(19,27)(20,25)(21,26)(34,38)(35,39)(36,37)(40,49)(41,50)(42,51)(43,56)(44,57)(45,55)(46,54)(47,52)(48,53)(61,65)(62,66)(63,64)(67,76)(68,77)(69,78)(70,83)(71,84)(72,82)(73,81)(74,79)(75,80); s3 := Sym(84)!( 4,13)( 5,15)( 6,14)( 7,16)( 8,18)( 9,17)(10,19)(11,21)(12,20)(23,24)(26,27)(29,30)(31,68)(32,67)(33,69)(34,71)(35,70)(36,72)(37,74)(38,73)(39,75)(40,59)(41,58)(42,60)(43,62)(44,61)(45,63)(46,65)(47,64)(48,66)(49,77)(50,76)(51,78)(52,80)(53,79)(54,81)(55,83)(56,82)(57,84); s4 := Sym(84)!( 4,31)( 5,33)( 6,32)( 7,36)( 8,35)( 9,34)(10,38)(11,37)(12,39)(13,56)(14,55)(15,57)(16,49)(17,51)(18,50)(19,54)(20,53)(21,52)(22,43)(23,45)(24,44)(25,48)(26,47)(27,46)(28,41)(29,40)(30,42)(58,59)(62,63)(64,66)(67,84)(68,83)(69,82)(70,77)(71,76)(72,78)(73,79)(74,81)(75,80); poly := sub<Sym(84)|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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, s2*s3*s2*s3*s4*s3*s2*s3*s4*s2*s3*s2*s4*s3*s2*s4*s3*s4 >;