Overview
- Group
- SmallGroup(1944,944)
- Rank
- 4
- Schläfli Type
- {2,6,18}
- Vertices, edges, …
- 2, 27, 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 := ( 6, 9)( 7,10)( 8,11)(12,22)(13,23)(14,21)(15,28)(16,29)(17,27)(18,25)(19,26)(20,24)(33,36)(34,37)(35,38)(39,49)(40,50)(41,48)(42,55)(43,56)(44,54)(45,52)(46,53)(47,51)(60,63)(61,64)(62,65)(66,76)(67,77)(68,75)(69,82)(70,83)(71,81)(72,79)(73,80)(74,78);; s2 := ( 4, 5)( 6, 9)( 7,11)( 8,10)(12,18)(13,20)(14,19)(16,17)(21,24)(22,26)(23,25)(28,29)(30,79)(31,78)(32,80)(33,76)(34,75)(35,77)(36,82)(37,81)(38,83)(39,58)(40,57)(41,59)(42,64)(43,63)(44,65)(45,61)(46,60)(47,62)(48,73)(49,72)(50,74)(51,70)(52,69)(53,71)(54,67)(55,66)(56,68);; s3 := ( 3,30)( 4,32)( 5,31)( 6,33)( 7,35)( 8,34)( 9,36)(10,38)(11,37)(12,48)(13,50)(14,49)(15,51)(16,53)(17,52)(18,54)(19,56)(20,55)(21,39)(22,41)(23,40)(24,42)(25,44)(26,43)(27,45)(28,47)(29,46)(57,58)(60,61)(63,64)(66,76)(67,75)(68,77)(69,79)(70,78)(71,80)(72,82)(73,81)(74,83);; 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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(83)!(1,2); s1 := Sym(83)!( 6, 9)( 7,10)( 8,11)(12,22)(13,23)(14,21)(15,28)(16,29)(17,27)(18,25)(19,26)(20,24)(33,36)(34,37)(35,38)(39,49)(40,50)(41,48)(42,55)(43,56)(44,54)(45,52)(46,53)(47,51)(60,63)(61,64)(62,65)(66,76)(67,77)(68,75)(69,82)(70,83)(71,81)(72,79)(73,80)(74,78); s2 := Sym(83)!( 4, 5)( 6, 9)( 7,11)( 8,10)(12,18)(13,20)(14,19)(16,17)(21,24)(22,26)(23,25)(28,29)(30,79)(31,78)(32,80)(33,76)(34,75)(35,77)(36,82)(37,81)(38,83)(39,58)(40,57)(41,59)(42,64)(43,63)(44,65)(45,61)(46,60)(47,62)(48,73)(49,72)(50,74)(51,70)(52,69)(53,71)(54,67)(55,66)(56,68); s3 := Sym(83)!( 3,30)( 4,32)( 5,31)( 6,33)( 7,35)( 8,34)( 9,36)(10,38)(11,37)(12,48)(13,50)(14,49)(15,51)(16,53)(17,52)(18,54)(19,56)(20,55)(21,39)(22,41)(23,40)(24,42)(25,44)(26,43)(27,45)(28,47)(29,46)(57,58)(60,61)(63,64)(66,76)(67,75)(68,77)(69,79)(70,78)(71,80)(72,82)(73,81)(74,83); 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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;