Overview
- Group
- SmallGroup(1728,47319)
- Rank
- 5
- Schläfli Type
- {6,2,12,6}
- Vertices, edges, …
- 6, 6, 12, 36, 6
- Order of s0s1s2s3s4
- 12
- Order of s0s1s2s3s4s3s2s1
- 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
24-fold
27-fold
36-fold
54-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (3,4)(5,6);; s1 := (1,5)(2,3)(4,6);; s2 := ( 7,43)( 8,44)( 9,45)(10,49)(11,50)(12,51)(13,46)(14,47)(15,48)(16,52)(17,53)(18,54)(19,58)(20,59)(21,60)(22,55)(23,56)(24,57)(25,70)(26,71)(27,72)(28,76)(29,77)(30,78)(31,73)(32,74)(33,75)(34,61)(35,62)(36,63)(37,67)(38,68)(39,69)(40,64)(41,65)(42,66);; s3 := ( 7,64)( 8,66)( 9,65)(10,61)(11,63)(12,62)(13,67)(14,69)(15,68)(16,73)(17,75)(18,74)(19,70)(20,72)(21,71)(22,76)(23,78)(24,77)(25,46)(26,48)(27,47)(28,43)(29,45)(30,44)(31,49)(32,51)(33,50)(34,55)(35,57)(36,56)(37,52)(38,54)(39,53)(40,58)(41,60)(42,59);; s4 := ( 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);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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,
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*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(78)!(3,4)(5,6); s1 := Sym(78)!(1,5)(2,3)(4,6); s2 := Sym(78)!( 7,43)( 8,44)( 9,45)(10,49)(11,50)(12,51)(13,46)(14,47)(15,48)(16,52)(17,53)(18,54)(19,58)(20,59)(21,60)(22,55)(23,56)(24,57)(25,70)(26,71)(27,72)(28,76)(29,77)(30,78)(31,73)(32,74)(33,75)(34,61)(35,62)(36,63)(37,67)(38,68)(39,69)(40,64)(41,65)(42,66); s3 := Sym(78)!( 7,64)( 8,66)( 9,65)(10,61)(11,63)(12,62)(13,67)(14,69)(15,68)(16,73)(17,75)(18,74)(19,70)(20,72)(21,71)(22,76)(23,78)(24,77)(25,46)(26,48)(27,47)(28,43)(29,45)(30,44)(31,49)(32,51)(33,50)(34,55)(35,57)(36,56)(37,52)(38,54)(39,53)(40,58)(41,60)(42,59); s4 := Sym(78)!( 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); poly := sub<Sym(78)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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, s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;