Overview
- Group
- SmallGroup(1296,2908)
- Rank
- 4
- Schläfli Type
- {6,4,18}
- Vertices, edges, …
- 9, 18, 54, 18
- Order of s0s1s2s3
- 36
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
9-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := (10,19)(11,20)(12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(28,55)(29,56)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,73)(38,74)(39,75)(40,76)(41,77)(42,78)(43,79)(44,80)(45,81)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72);; s1 := ( 1,28)( 2,29)( 3,30)( 4,31)( 5,32)( 6,33)( 7,34)( 8,35)( 9,36)(10,37)(11,38)(12,39)(13,40)(14,41)(15,42)(16,43)(17,44)(18,45)(19,46)(20,47)(21,48)(22,49)(23,50)(24,51)(25,52)(26,53)(27,54);; s2 := ( 2, 3)( 4, 8)( 5, 7)( 6, 9)(10,28)(11,30)(12,29)(13,35)(14,34)(15,36)(16,32)(17,31)(18,33)(19,55)(20,57)(21,56)(22,62)(23,61)(24,63)(25,59)(26,58)(27,60)(38,39)(40,44)(41,43)(42,45)(46,64)(47,66)(48,65)(49,71)(50,70)(51,72)(52,68)(53,67)(54,69)(74,75)(76,80)(77,79)(78,81);; s3 := ( 1, 4)( 2, 6)( 3, 5)( 7, 8)(10,13)(11,15)(12,14)(16,17)(19,22)(20,24)(21,23)(25,26)(28,31)(29,33)(30,32)(34,35)(37,40)(38,42)(39,41)(43,44)(46,49)(47,51)(48,50)(52,53)(55,58)(56,60)(57,59)(61,62)(64,67)(65,69)(66,68)(70,71)(73,76)(74,78)(75,77)(79,80);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*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*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(81)!(10,19)(11,20)(12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(28,55)(29,56)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,73)(38,74)(39,75)(40,76)(41,77)(42,78)(43,79)(44,80)(45,81)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72); s1 := Sym(81)!( 1,28)( 2,29)( 3,30)( 4,31)( 5,32)( 6,33)( 7,34)( 8,35)( 9,36)(10,37)(11,38)(12,39)(13,40)(14,41)(15,42)(16,43)(17,44)(18,45)(19,46)(20,47)(21,48)(22,49)(23,50)(24,51)(25,52)(26,53)(27,54); s2 := Sym(81)!( 2, 3)( 4, 8)( 5, 7)( 6, 9)(10,28)(11,30)(12,29)(13,35)(14,34)(15,36)(16,32)(17,31)(18,33)(19,55)(20,57)(21,56)(22,62)(23,61)(24,63)(25,59)(26,58)(27,60)(38,39)(40,44)(41,43)(42,45)(46,64)(47,66)(48,65)(49,71)(50,70)(51,72)(52,68)(53,67)(54,69)(74,75)(76,80)(77,79)(78,81); s3 := Sym(81)!( 1, 4)( 2, 6)( 3, 5)( 7, 8)(10,13)(11,15)(12,14)(16,17)(19,22)(20,24)(21,23)(25,26)(28,31)(29,33)(30,32)(34,35)(37,40)(38,42)(39,41)(43,44)(46,49)(47,51)(48,50)(52,53)(55,58)(56,60)(57,59)(61,62)(64,67)(65,69)(66,68)(70,71)(73,76)(74,78)(75,77)(79,80); poly := sub<Sym(81)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*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*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.