Overview
- Group
- SmallGroup(1296,2976)
- Rank
- 4
- Schläfli Type
- {2,36,6}
- Vertices, edges, …
- 2, 54, 162, 9
- Order of s0s1s2s3
- 36
- 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)( 6,11)( 7,10)( 8, 9)(12,66)(13,68)(14,67)(15,74)(16,73)(17,72)(18,71)(19,70)(20,69)(21,48)(22,50)(23,49)(24,56)(25,55)(26,54)(27,53)(28,52)(29,51)(30,57)(31,59)(32,58)(33,65)(34,64)(35,63)(36,62)(37,61)(38,60)(40,41)(42,47)(43,46)(44,45)(76,77)(78,83)(79,82)(80,81);; s2 := ( 3, 6)( 4, 8)( 5, 7)( 9,11)(12,24)(13,26)(14,25)(15,21)(16,23)(17,22)(18,29)(19,28)(20,27)(30,42)(31,44)(32,43)(33,39)(34,41)(35,40)(36,47)(37,46)(38,45)(48,51)(49,53)(50,52)(54,56)(57,78)(58,80)(59,79)(60,75)(61,77)(62,76)(63,83)(64,82)(65,81)(66,69)(67,71)(68,70)(72,74);; s3 := ( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,48)(22,49)(23,50)(24,51)(25,52)(26,53)(27,54)(28,55)(29,56)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74);; 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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(83)!(1,2); s1 := Sym(83)!( 4, 5)( 6,11)( 7,10)( 8, 9)(12,66)(13,68)(14,67)(15,74)(16,73)(17,72)(18,71)(19,70)(20,69)(21,48)(22,50)(23,49)(24,56)(25,55)(26,54)(27,53)(28,52)(29,51)(30,57)(31,59)(32,58)(33,65)(34,64)(35,63)(36,62)(37,61)(38,60)(40,41)(42,47)(43,46)(44,45)(76,77)(78,83)(79,82)(80,81); s2 := Sym(83)!( 3, 6)( 4, 8)( 5, 7)( 9,11)(12,24)(13,26)(14,25)(15,21)(16,23)(17,22)(18,29)(19,28)(20,27)(30,42)(31,44)(32,43)(33,39)(34,41)(35,40)(36,47)(37,46)(38,45)(48,51)(49,53)(50,52)(54,56)(57,78)(58,80)(59,79)(60,75)(61,77)(62,76)(63,83)(64,82)(65,81)(66,69)(67,71)(68,70)(72,74); s3 := Sym(83)!( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,48)(22,49)(23,50)(24,51)(25,52)(26,53)(27,54)(28,55)(29,56)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74); 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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2 >;