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