Overview
- Group
- SmallGroup(1944,941)
- Rank
- 4
- Schläfli Type
- {2,6,6}
- Vertices, edges, …
- 2, 81, 243, 81
- Order of s0s1s2s3
- 18
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
9-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7, 8)(10,11)(12,24)(13,26)(14,25)(15,27)(16,29)(17,28)(18,21)(19,23)(20,22)(30,57)(31,59)(32,58)(33,60)(34,62)(35,61)(36,63)(37,65)(38,64)(39,78)(40,80)(41,79)(42,81)(43,83)(44,82)(45,75)(46,77)(47,76)(48,72)(49,74)(50,73)(51,66)(52,68)(53,67)(54,69)(55,71)(56,70);; s2 := ( 3,30)( 4,32)( 5,31)( 6,36)( 7,38)( 8,37)( 9,33)(10,35)(11,34)(12,41)(13,40)(14,39)(15,47)(16,46)(17,45)(18,44)(19,43)(20,42)(21,49)(22,48)(23,50)(24,55)(25,54)(26,56)(27,52)(28,51)(29,53)(58,59)(60,63)(61,65)(62,64)(66,68)(69,74)(70,73)(71,72)(75,76)(78,82)(79,81)(80,83);; s3 := ( 6, 9)( 7,10)( 8,11)(12,21)(13,22)(14,23)(15,27)(16,28)(17,29)(18,24)(19,25)(20,26)(30,39)(31,40)(32,41)(33,45)(34,46)(35,47)(36,42)(37,43)(38,44)(51,54)(52,55)(53,56)(57,78)(58,79)(59,80)(60,75)(61,76)(62,77)(63,81)(64,82)(65,83)(66,69)(67,70)(68,71);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1,
s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(83)!(1,2); s1 := Sym(83)!( 4, 5)( 7, 8)(10,11)(12,24)(13,26)(14,25)(15,27)(16,29)(17,28)(18,21)(19,23)(20,22)(30,57)(31,59)(32,58)(33,60)(34,62)(35,61)(36,63)(37,65)(38,64)(39,78)(40,80)(41,79)(42,81)(43,83)(44,82)(45,75)(46,77)(47,76)(48,72)(49,74)(50,73)(51,66)(52,68)(53,67)(54,69)(55,71)(56,70); s2 := Sym(83)!( 3,30)( 4,32)( 5,31)( 6,36)( 7,38)( 8,37)( 9,33)(10,35)(11,34)(12,41)(13,40)(14,39)(15,47)(16,46)(17,45)(18,44)(19,43)(20,42)(21,49)(22,48)(23,50)(24,55)(25,54)(26,56)(27,52)(28,51)(29,53)(58,59)(60,63)(61,65)(62,64)(66,68)(69,74)(70,73)(71,72)(75,76)(78,82)(79,81)(80,83); s3 := Sym(83)!( 6, 9)( 7,10)( 8,11)(12,21)(13,22)(14,23)(15,27)(16,28)(17,29)(18,24)(19,25)(20,26)(30,39)(31,40)(32,41)(33,45)(34,46)(35,47)(36,42)(37,43)(38,44)(51,54)(52,55)(53,56)(57,78)(58,79)(59,80)(60,75)(61,76)(62,77)(63,81)(64,82)(65,83)(66,69)(67,70)(68,71); poly := sub<Sym(83)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1, s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2, s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 >;