Overview
- Group
- SmallGroup(1728,47319)
- Rank
- 6
- Schläfli Type
- {3,2,6,12,2}
- Vertices, edges, …
- 3, 3, 6, 36, 12, 2
- 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 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72)(74,75);; s3 := ( 4,41)( 5,40)( 6,42)( 7,47)( 8,46)( 9,48)(10,44)(11,43)(12,45)(13,50)(14,49)(15,51)(16,56)(17,55)(18,57)(19,53)(20,52)(21,54)(22,68)(23,67)(24,69)(25,74)(26,73)(27,75)(28,71)(29,70)(30,72)(31,59)(32,58)(33,60)(34,65)(35,64)(36,66)(37,62)(38,61)(39,63);; s4 := ( 4,61)( 5,63)( 6,62)( 7,58)( 8,60)( 9,59)(10,64)(11,66)(12,65)(13,70)(14,72)(15,71)(16,67)(17,69)(18,68)(19,73)(20,75)(21,74)(22,43)(23,45)(24,44)(25,40)(26,42)(27,41)(28,46)(29,48)(30,47)(31,52)(32,54)(33,53)(34,49)(35,51)(36,50)(37,55)(38,57)(39,56);; 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, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(77)!(2,3); s1 := Sym(77)!(1,2); s2 := Sym(77)!( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72)(74,75); s3 := Sym(77)!( 4,41)( 5,40)( 6,42)( 7,47)( 8,46)( 9,48)(10,44)(11,43)(12,45)(13,50)(14,49)(15,51)(16,56)(17,55)(18,57)(19,53)(20,52)(21,54)(22,68)(23,67)(24,69)(25,74)(26,73)(27,75)(28,71)(29,70)(30,72)(31,59)(32,58)(33,60)(34,65)(35,64)(36,66)(37,62)(38,61)(39,63); s4 := Sym(77)!( 4,61)( 5,63)( 6,62)( 7,58)( 8,60)( 9,59)(10,64)(11,66)(12,65)(13,70)(14,72)(15,71)(16,67)(17,69)(18,68)(19,73)(20,75)(21,74)(22,43)(23,45)(24,44)(25,40)(26,42)(27,41)(28,46)(29,48)(30,47)(31,52)(32,54)(33,53)(34,49)(35,51)(36,50)(37,55)(38,57)(39,56); 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, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;