Overview
- Group
- SmallGroup(1344,11661)
- Rank
- 5
- Schläfli Type
- {2,4,42,2}
- Vertices, edges, …
- 2, 4, 84, 42, 2
- Order of s0s1s2s3s4
- 84
- 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
7-fold
12-fold
14-fold
21-fold
28-fold
42-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (45,66)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,75)(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86);; s2 := ( 3,45)( 4,51)( 5,50)( 6,49)( 7,48)( 8,47)( 9,46)(10,59)(11,65)(12,64)(13,63)(14,62)(15,61)(16,60)(17,52)(18,58)(19,57)(20,56)(21,55)(22,54)(23,53)(24,66)(25,72)(26,71)(27,70)(28,69)(29,68)(30,67)(31,80)(32,86)(33,85)(34,84)(35,83)(36,82)(37,81)(38,73)(39,79)(40,78)(41,77)(42,76)(43,75)(44,74);; s3 := ( 3,11)( 4,10)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(17,18)(19,23)(20,22)(24,32)(25,31)(26,37)(27,36)(28,35)(29,34)(30,33)(38,39)(40,44)(41,43)(45,53)(46,52)(47,58)(48,57)(49,56)(50,55)(51,54)(59,60)(61,65)(62,64)(66,74)(67,73)(68,79)(69,78)(70,77)(71,76)(72,75)(80,81)(82,86)(83,85);; s4 := (87,88);; 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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, 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*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(88)!(1,2); s1 := Sym(88)!(45,66)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,75)(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86); s2 := Sym(88)!( 3,45)( 4,51)( 5,50)( 6,49)( 7,48)( 8,47)( 9,46)(10,59)(11,65)(12,64)(13,63)(14,62)(15,61)(16,60)(17,52)(18,58)(19,57)(20,56)(21,55)(22,54)(23,53)(24,66)(25,72)(26,71)(27,70)(28,69)(29,68)(30,67)(31,80)(32,86)(33,85)(34,84)(35,83)(36,82)(37,81)(38,73)(39,79)(40,78)(41,77)(42,76)(43,75)(44,74); s3 := Sym(88)!( 3,11)( 4,10)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(17,18)(19,23)(20,22)(24,32)(25,31)(26,37)(27,36)(28,35)(29,34)(30,33)(38,39)(40,44)(41,43)(45,53)(46,52)(47,58)(48,57)(49,56)(50,55)(51,54)(59,60)(61,65)(62,64)(66,74)(67,73)(68,79)(69,78)(70,77)(71,76)(72,75)(80,81)(82,86)(83,85); s4 := Sym(88)!(87,88); poly := sub<Sym(88)|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, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 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*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 >;