Overview
- Group
- SmallGroup(1944,2345)
- Rank
- 5
- Schläfli Type
- {3,2,9,6}
- Vertices, edges, …
- 3, 3, 27, 81, 18
- 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 := ( 5, 6)( 7, 9)(10,11)(13,22)(14,24)(15,23)(16,27)(17,26)(18,25)(19,29)(20,28)(21,30)(31,59)(32,58)(33,60)(34,61)(35,63)(36,62)(37,66)(38,65)(39,64)(40,77)(41,76)(42,78)(43,79)(44,81)(45,80)(46,84)(47,83)(48,82)(49,68)(50,67)(51,69)(52,70)(53,72)(54,71)(55,75)(56,74)(57,73);; s3 := ( 4,46)( 5,48)( 6,47)( 7,40)( 8,42)( 9,41)(10,43)(11,45)(12,44)(13,34)(14,36)(15,35)(16,37)(17,39)(18,38)(19,31)(20,33)(21,32)(22,50)(23,49)(24,51)(25,53)(26,52)(27,54)(28,56)(29,55)(30,57)(58,74)(59,73)(60,75)(61,68)(62,67)(63,69)(64,71)(65,70)(66,72)(76,78)(79,81)(82,84);; s4 := ( 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);; 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*s4*s3*s2*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s2*s4*s3*s4*s3*s2*s3*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4,
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(84)!(2,3); s1 := Sym(84)!(1,2); s2 := Sym(84)!( 5, 6)( 7, 9)(10,11)(13,22)(14,24)(15,23)(16,27)(17,26)(18,25)(19,29)(20,28)(21,30)(31,59)(32,58)(33,60)(34,61)(35,63)(36,62)(37,66)(38,65)(39,64)(40,77)(41,76)(42,78)(43,79)(44,81)(45,80)(46,84)(47,83)(48,82)(49,68)(50,67)(51,69)(52,70)(53,72)(54,71)(55,75)(56,74)(57,73); s3 := Sym(84)!( 4,46)( 5,48)( 6,47)( 7,40)( 8,42)( 9,41)(10,43)(11,45)(12,44)(13,34)(14,36)(15,35)(16,37)(17,39)(18,38)(19,31)(20,33)(21,32)(22,50)(23,49)(24,51)(25,53)(26,52)(27,54)(28,56)(29,55)(30,57)(58,74)(59,73)(60,75)(61,68)(62,67)(63,69)(64,71)(65,70)(66,72)(76,78)(79,81)(82,84); s4 := 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); 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*s4*s3*s2*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s3*s2*s4*s3*s4*s3*s2*s3*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;