Overview
- Group
- SmallGroup(1728,46115)
- Rank
- 6
- Schläfli Type
- {2,3,2,4,9}
- Vertices, edges, …
- 2, 3, 3, 8, 36, 18
- 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 := (1,2);; s1 := (4,5);; s2 := (3,4);; s3 := ( 6,43)( 7,42)( 8,45)( 9,44)(10,47)(11,46)(12,49)(13,48)(14,51)(15,50)(16,53)(17,52)(18,55)(19,54)(20,57)(21,56)(22,59)(23,58)(24,61)(25,60)(26,63)(27,62)(28,65)(29,64)(30,67)(31,66)(32,69)(33,68)(34,71)(35,70)(36,73)(37,72)(38,75)(39,74)(40,77)(41,76);; s4 := ( 7, 8)(10,14)(11,16)(12,15)(13,17)(18,34)(19,36)(20,35)(21,37)(22,30)(23,32)(24,31)(25,33)(26,38)(27,40)(28,39)(29,41)(43,44)(46,50)(47,52)(48,51)(49,53)(54,70)(55,72)(56,71)(57,73)(58,66)(59,68)(60,67)(61,69)(62,74)(63,76)(64,75)(65,77);; s5 := ( 6,18)( 7,19)( 8,21)( 9,20)(10,26)(11,27)(12,29)(13,28)(14,22)(15,23)(16,25)(17,24)(30,34)(31,35)(32,37)(33,36)(40,41)(42,54)(43,55)(44,57)(45,56)(46,62)(47,63)(48,65)(49,64)(50,58)(51,59)(52,61)(53,60)(66,70)(67,71)(68,73)(69,72)(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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*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,
s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s5*s4*s5*s4*s3*s4*s5*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(77)!(1,2); s1 := Sym(77)!(4,5); s2 := Sym(77)!(3,4); s3 := Sym(77)!( 6,43)( 7,42)( 8,45)( 9,44)(10,47)(11,46)(12,49)(13,48)(14,51)(15,50)(16,53)(17,52)(18,55)(19,54)(20,57)(21,56)(22,59)(23,58)(24,61)(25,60)(26,63)(27,62)(28,65)(29,64)(30,67)(31,66)(32,69)(33,68)(34,71)(35,70)(36,73)(37,72)(38,75)(39,74)(40,77)(41,76); s4 := Sym(77)!( 7, 8)(10,14)(11,16)(12,15)(13,17)(18,34)(19,36)(20,35)(21,37)(22,30)(23,32)(24,31)(25,33)(26,38)(27,40)(28,39)(29,41)(43,44)(46,50)(47,52)(48,51)(49,53)(54,70)(55,72)(56,71)(57,73)(58,66)(59,68)(60,67)(61,69)(62,74)(63,76)(64,75)(65,77); s5 := Sym(77)!( 6,18)( 7,19)( 8,21)( 9,20)(10,26)(11,27)(12,29)(13,28)(14,22)(15,23)(16,25)(17,24)(30,34)(31,35)(32,37)(33,36)(40,41)(42,54)(43,55)(44,57)(45,56)(46,62)(47,63)(48,65)(49,64)(50,58)(51,59)(52,61)(53,60)(66,70)(67,71)(68,73)(69,72)(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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*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, s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s5*s4*s3*s4*s5*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;