Overview
- Group
- SmallGroup(1680,966)
- Rank
- 5
- Schläfli Type
- {3,2,10,14}
- Vertices, edges, …
- 3, 3, 10, 70, 14
- Order of s0s1s2s3s4
- 210
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
5-fold
7-fold
10-fold
14-fold
35-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := (11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,25)(19,26)(20,27)(21,28)(22,29)(23,30)(24,31)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65)(59,66);; s3 := ( 4,11)( 5,17)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(18,32)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(26,31)(27,30)(28,29)(39,46)(40,52)(41,51)(42,50)(43,49)(44,48)(45,47)(53,67)(54,73)(55,72)(56,71)(57,70)(58,69)(59,68)(61,66)(62,65)(63,64);; s4 := ( 4,40)( 5,39)( 6,45)( 7,44)( 8,43)( 9,42)(10,41)(11,47)(12,46)(13,52)(14,51)(15,50)(16,49)(17,48)(18,54)(19,53)(20,59)(21,58)(22,57)(23,56)(24,55)(25,61)(26,60)(27,66)(28,65)(29,64)(30,63)(31,62)(32,68)(33,67)(34,73)(35,72)(36,71)(37,70)(38,69);; 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,
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*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*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(73)!(2,3); s1 := Sym(73)!(1,2); s2 := Sym(73)!(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,25)(19,26)(20,27)(21,28)(22,29)(23,30)(24,31)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65)(59,66); s3 := Sym(73)!( 4,11)( 5,17)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(18,32)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(26,31)(27,30)(28,29)(39,46)(40,52)(41,51)(42,50)(43,49)(44,48)(45,47)(53,67)(54,73)(55,72)(56,71)(57,70)(58,69)(59,68)(61,66)(62,65)(63,64); s4 := Sym(73)!( 4,40)( 5,39)( 6,45)( 7,44)( 8,43)( 9,42)(10,41)(11,47)(12,46)(13,52)(14,51)(15,50)(16,49)(17,48)(18,54)(19,53)(20,59)(21,58)(22,57)(23,56)(24,55)(25,61)(26,60)(27,66)(28,65)(29,64)(30,63)(31,62)(32,68)(33,67)(34,73)(35,72)(36,71)(37,70)(38,69); poly := sub<Sym(73)|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, s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*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*s3*s4*s3*s4 >;