Overview
- Group
- SmallGroup(1728,46115)
- Rank
- 6
- Schläfli Type
- {3,2,9,4,2}
- Vertices, edges, …
- 3, 3, 18, 36, 8, 2
- Order of s0s1s2s3s4s5
- 18
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
12-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 5, 6)( 8,12)( 9,14)(10,13)(11,15)(16,32)(17,34)(18,33)(19,35)(20,28)(21,30)(22,29)(23,31)(24,36)(25,38)(26,37)(27,39)(41,42)(44,48)(45,50)(46,49)(47,51)(52,68)(53,70)(54,69)(55,71)(56,64)(57,66)(58,65)(59,67)(60,72)(61,74)(62,73)(63,75);; s3 := ( 4,16)( 5,17)( 6,19)( 7,18)( 8,24)( 9,25)(10,27)(11,26)(12,20)(13,21)(14,23)(15,22)(28,32)(29,33)(30,35)(31,34)(38,39)(40,52)(41,53)(42,55)(43,54)(44,60)(45,61)(46,63)(47,62)(48,56)(49,57)(50,59)(51,58)(64,68)(65,69)(66,71)(67,70)(74,75);; s4 := ( 4,43)( 5,42)( 6,41)( 7,40)( 8,47)( 9,46)(10,45)(11,44)(12,51)(13,50)(14,49)(15,48)(16,55)(17,54)(18,53)(19,52)(20,59)(21,58)(22,57)(23,56)(24,63)(25,62)(26,61)(27,60)(28,67)(29,66)(30,65)(31,64)(32,71)(33,70)(34,69)(35,68)(36,75)(37,74)(38,73)(39,72);; s5 := (76,77);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*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(77)!(2,3); s1 := Sym(77)!(1,2); s2 := Sym(77)!( 5, 6)( 8,12)( 9,14)(10,13)(11,15)(16,32)(17,34)(18,33)(19,35)(20,28)(21,30)(22,29)(23,31)(24,36)(25,38)(26,37)(27,39)(41,42)(44,48)(45,50)(46,49)(47,51)(52,68)(53,70)(54,69)(55,71)(56,64)(57,66)(58,65)(59,67)(60,72)(61,74)(62,73)(63,75); s3 := Sym(77)!( 4,16)( 5,17)( 6,19)( 7,18)( 8,24)( 9,25)(10,27)(11,26)(12,20)(13,21)(14,23)(15,22)(28,32)(29,33)(30,35)(31,34)(38,39)(40,52)(41,53)(42,55)(43,54)(44,60)(45,61)(46,63)(47,62)(48,56)(49,57)(50,59)(51,58)(64,68)(65,69)(66,71)(67,70)(74,75); s4 := Sym(77)!( 4,43)( 5,42)( 6,41)( 7,40)( 8,47)( 9,46)(10,45)(11,44)(12,51)(13,50)(14,49)(15,48)(16,55)(17,54)(18,53)(19,52)(20,59)(21,58)(22,57)(23,56)(24,63)(25,62)(26,61)(27,60)(28,67)(29,66)(30,65)(31,64)(32,71)(33,70)(34,69)(35,68)(36,75)(37,74)(38,73)(39,72); s5 := Sym(77)!(76,77); poly := sub<Sym(77)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;