Overview
- Group
- SmallGroup(1728,47319)
- Rank
- 6
- Schläfli Type
- {3,2,2,6,12}
- Vertices, edges, …
- 3, 3, 2, 6, 36, 12
- Order of s0s1s2s3s4s5
- 12
- 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
9-fold
12-fold
18-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := (4,5);; s3 := ( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74)(76,77);; s4 := ( 6,43)( 7,42)( 8,44)( 9,49)(10,48)(11,50)(12,46)(13,45)(14,47)(15,52)(16,51)(17,53)(18,58)(19,57)(20,59)(21,55)(22,54)(23,56)(24,70)(25,69)(26,71)(27,76)(28,75)(29,77)(30,73)(31,72)(32,74)(33,61)(34,60)(35,62)(36,67)(37,66)(38,68)(39,64)(40,63)(41,65);; s5 := ( 6,63)( 7,65)( 8,64)( 9,60)(10,62)(11,61)(12,66)(13,68)(14,67)(15,72)(16,74)(17,73)(18,69)(19,71)(20,70)(21,75)(22,77)(23,76)(24,45)(25,47)(26,46)(27,42)(28,44)(29,43)(30,48)(31,50)(32,49)(33,54)(34,56)(35,55)(36,51)(37,53)(38,52)(39,57)(40,59)(41,58);; 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, 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,
s0*s1*s0*s1*s0*s1, s3*s4*s5*s3*s4*s3*s4*s5*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*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)!(2,3); s1 := Sym(77)!(1,2); s2 := Sym(77)!(4,5); s3 := Sym(77)!( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74)(76,77); s4 := Sym(77)!( 6,43)( 7,42)( 8,44)( 9,49)(10,48)(11,50)(12,46)(13,45)(14,47)(15,52)(16,51)(17,53)(18,58)(19,57)(20,59)(21,55)(22,54)(23,56)(24,70)(25,69)(26,71)(27,76)(28,75)(29,77)(30,73)(31,72)(32,74)(33,61)(34,60)(35,62)(36,67)(37,66)(38,68)(39,64)(40,63)(41,65); s5 := Sym(77)!( 6,63)( 7,65)( 8,64)( 9,60)(10,62)(11,61)(12,66)(13,68)(14,67)(15,72)(16,74)(17,73)(18,69)(19,71)(20,70)(21,75)(22,77)(23,76)(24,45)(25,47)(26,46)(27,42)(28,44)(29,43)(30,48)(31,50)(32,49)(33,54)(34,56)(35,55)(36,51)(37,53)(38,52)(39,57)(40,59)(41,58); 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, 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, s0*s1*s0*s1*s0*s1, s3*s4*s5*s3*s4*s3*s4*s5*s3*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;