Overview
- Group
- SmallGroup(1872,1061)
- Rank
- 5
- Schläfli Type
- {3,2,26,6}
- Vertices, edges, …
- 3, 3, 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 := (2,3);; s1 := (1,2);; s2 := ( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63)(70,81)(71,80)(72,79)(73,78)(74,77)(75,76);; s3 := ( 4, 5)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(17,31)(18,30)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(43,44)(45,55)(46,54)(47,53)(48,52)(49,51)(56,70)(57,69)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71);; s4 := ( 4,56)( 5,57)( 6,58)( 7,59)( 8,60)( 9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,68)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(27,53)(28,54)(29,55)(30,69)(31,70)(32,71)(33,72)(34,73)(35,74)(36,75)(37,76)(38,77)(39,78)(40,79)(41,80)(42,81);; 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,
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(81)!(2,3); s1 := Sym(81)!(1,2); s2 := Sym(81)!( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63)(70,81)(71,80)(72,79)(73,78)(74,77)(75,76); s3 := Sym(81)!( 4, 5)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(17,31)(18,30)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(43,44)(45,55)(46,54)(47,53)(48,52)(49,51)(56,70)(57,69)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71); s4 := Sym(81)!( 4,56)( 5,57)( 6,58)( 7,59)( 8,60)( 9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,68)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(27,53)(28,54)(29,55)(30,69)(31,70)(32,71)(33,72)(34,73)(35,74)(36,75)(37,76)(38,77)(39,78)(40,79)(41,80)(42,81); poly := sub<Sym(81)|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, 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 >;