Overview
- Group
- SmallGroup(1944,2340)
- Rank
- 5
- Schläfli Type
- {3,2,18,6}
- Vertices, edges, …
- 3, 3, 27, 81, 9
- Order of s0s1s2s3s4
- 9
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 5, 6)( 7,10)( 8,12)( 9,11)(14,15)(16,19)(17,21)(18,20)(23,24)(25,28)(26,30)(27,29)(31,61)(32,63)(33,62)(34,58)(35,60)(36,59)(37,64)(38,66)(39,65)(40,70)(41,72)(42,71)(43,67)(44,69)(45,68)(46,73)(47,75)(48,74)(49,79)(50,81)(51,80)(52,76)(53,78)(54,77)(55,82)(56,84)(57,83);; s3 := ( 4,31)( 5,32)( 6,33)( 7,37)( 8,38)( 9,39)(10,34)(11,35)(12,36)(13,51)(14,49)(15,50)(16,57)(17,55)(18,56)(19,54)(20,52)(21,53)(22,41)(23,42)(24,40)(25,47)(26,48)(27,46)(28,44)(29,45)(30,43)(58,61)(59,62)(60,63)(67,81)(68,79)(69,80)(70,78)(71,76)(72,77)(73,84)(74,82)(75,83);; s4 := ( 4,13)( 5,15)( 6,14)( 7,16)( 8,18)( 9,17)(10,19)(11,21)(12,20)(23,24)(26,27)(29,30)(31,40)(32,42)(33,41)(34,43)(35,45)(36,44)(37,46)(38,48)(39,47)(50,51)(53,54)(56,57)(58,67)(59,69)(60,68)(61,70)(62,72)(63,71)(64,73)(65,75)(66,74)(77,78)(80,81)(83,84);; 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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(84)!(2,3); s1 := Sym(84)!(1,2); s2 := Sym(84)!( 5, 6)( 7,10)( 8,12)( 9,11)(14,15)(16,19)(17,21)(18,20)(23,24)(25,28)(26,30)(27,29)(31,61)(32,63)(33,62)(34,58)(35,60)(36,59)(37,64)(38,66)(39,65)(40,70)(41,72)(42,71)(43,67)(44,69)(45,68)(46,73)(47,75)(48,74)(49,79)(50,81)(51,80)(52,76)(53,78)(54,77)(55,82)(56,84)(57,83); s3 := Sym(84)!( 4,31)( 5,32)( 6,33)( 7,37)( 8,38)( 9,39)(10,34)(11,35)(12,36)(13,51)(14,49)(15,50)(16,57)(17,55)(18,56)(19,54)(20,52)(21,53)(22,41)(23,42)(24,40)(25,47)(26,48)(27,46)(28,44)(29,45)(30,43)(58,61)(59,62)(60,63)(67,81)(68,79)(69,80)(70,78)(71,76)(72,77)(73,84)(74,82)(75,83); s4 := 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)(31,40)(32,42)(33,41)(34,43)(35,45)(36,44)(37,46)(38,48)(39,47)(50,51)(53,54)(56,57)(58,67)(59,69)(60,68)(61,70)(62,72)(63,71)(64,73)(65,75)(66,74)(77,78)(80,81)(83,84); 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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2*s3 >;