Overview
- Group
- SmallGroup(1944,2340)
- Rank
- 5
- Schläfli Type
- {3,2,6,18}
- Vertices, edges, …
- 3, 3, 9, 81, 27
- 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)( 8, 9)(11,12)(13,22)(14,24)(15,23)(16,25)(17,27)(18,26)(19,28)(20,30)(21,29)(32,33)(35,36)(38,39)(40,49)(41,51)(42,50)(43,52)(44,54)(45,53)(46,55)(47,57)(48,56)(59,60)(62,63)(65,66)(67,76)(68,78)(69,77)(70,79)(71,81)(72,80)(73,82)(74,84)(75,83);; s3 := ( 4,13)( 5,14)( 6,15)( 7,19)( 8,20)( 9,21)(10,16)(11,17)(12,18)(25,28)(26,29)(27,30)(31,70)(32,71)(33,72)(34,67)(35,68)(36,69)(37,73)(38,74)(39,75)(40,61)(41,62)(42,63)(43,58)(44,59)(45,60)(46,64)(47,65)(48,66)(49,79)(50,80)(51,81)(52,76)(53,77)(54,78)(55,82)(56,83)(57,84);; s4 := ( 4,31)( 5,33)( 6,32)( 7,37)( 8,39)( 9,38)(10,34)(11,36)(12,35)(13,41)(14,40)(15,42)(16,47)(17,46)(18,48)(19,44)(20,43)(21,45)(22,51)(23,50)(24,49)(25,57)(26,56)(27,55)(28,54)(29,53)(30,52)(58,61)(59,63)(60,62)(65,66)(67,71)(68,70)(69,72)(73,74)(76,81)(77,80)(78,79)(82,84);; 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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(84)!(2,3); s1 := Sym(84)!(1,2); s2 := Sym(84)!( 5, 6)( 8, 9)(11,12)(13,22)(14,24)(15,23)(16,25)(17,27)(18,26)(19,28)(20,30)(21,29)(32,33)(35,36)(38,39)(40,49)(41,51)(42,50)(43,52)(44,54)(45,53)(46,55)(47,57)(48,56)(59,60)(62,63)(65,66)(67,76)(68,78)(69,77)(70,79)(71,81)(72,80)(73,82)(74,84)(75,83); s3 := Sym(84)!( 4,13)( 5,14)( 6,15)( 7,19)( 8,20)( 9,21)(10,16)(11,17)(12,18)(25,28)(26,29)(27,30)(31,70)(32,71)(33,72)(34,67)(35,68)(36,69)(37,73)(38,74)(39,75)(40,61)(41,62)(42,63)(43,58)(44,59)(45,60)(46,64)(47,65)(48,66)(49,79)(50,80)(51,81)(52,76)(53,77)(54,78)(55,82)(56,83)(57,84); s4 := Sym(84)!( 4,31)( 5,33)( 6,32)( 7,37)( 8,39)( 9,38)(10,34)(11,36)(12,35)(13,41)(14,40)(15,42)(16,47)(17,46)(18,48)(19,44)(20,43)(21,45)(22,51)(23,50)(24,49)(25,57)(26,56)(27,55)(28,54)(29,53)(30,52)(58,61)(59,63)(60,62)(65,66)(67,71)(68,70)(69,72)(73,74)(76,81)(77,80)(78,79)(82,84); 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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s4*s3*s4 >;