Overview
- Group
- SmallGroup(1248,1451)
- Rank
- 5
- Schläfli Type
- {2,2,26,6}
- Vertices, edges, …
- 2, 2, 26, 78, 6
- Order of s0s1s2s3s4
- 78
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
6-fold
13-fold
26-fold
39-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := ( 6,17)( 7,16)( 8,15)( 9,14)(10,13)(11,12)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,82)(72,81)(73,80)(74,79)(75,78)(76,77);; s3 := ( 5, 6)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(18,32)(19,31)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(44,45)(46,56)(47,55)(48,54)(49,53)(50,52)(57,71)(58,70)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72);; s4 := ( 5,57)( 6,58)( 7,59)( 8,60)( 9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,68)(17,69)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(27,53)(28,54)(29,55)(30,56)(31,70)(32,71)(33,72)(34,73)(35,74)(36,75)(37,76)(38,77)(39,78)(40,79)(41,80)(42,81)(43,82);; 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*s1*s0*s1,
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,
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*s2*s3*s2*s3*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(82)!(1,2); s1 := Sym(82)!(3,4); s2 := Sym(82)!( 6,17)( 7,16)( 8,15)( 9,14)(10,13)(11,12)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,82)(72,81)(73,80)(74,79)(75,78)(76,77); s3 := Sym(82)!( 5, 6)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(18,32)(19,31)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(44,45)(46,56)(47,55)(48,54)(49,53)(50,52)(57,71)(58,70)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72); s4 := Sym(82)!( 5,57)( 6,58)( 7,59)( 8,60)( 9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,68)(17,69)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(27,53)(28,54)(29,55)(30,56)(31,70)(32,71)(33,72)(34,73)(35,74)(36,75)(37,76)(38,77)(39,78)(40,79)(41,80)(42,81)(43,82); poly := sub<Sym(82)|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*s1*s0*s1, 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, 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;