Polytope of Type {2,2,4,10,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,10,4}*1280
if this polytope has a name.
Group : SmallGroup(1280,1076475)
Rank : 6
Schlafli Type : {2,2,4,10,4}
Number of vertices, edges, etc : 2, 2, 4, 20, 20, 4
Order of s0s1s2s3s4s5 : 20
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,10,4}*640, {2,2,4,10,2}*640
4-fold quotients : {2,2,2,10,2}*320
5-fold quotients : {2,2,4,2,4}*256
8-fold quotients : {2,2,2,5,2}*160
10-fold quotients : {2,2,2,2,4}*128, {2,2,4,2,2}*128
20-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(54,64)
(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83)(74,84);;
s3 := ( 5,45)( 6,49)( 7,48)( 8,47)( 9,46)(10,50)(11,54)(12,53)(13,52)(14,51)
(15,55)(16,59)(17,58)(18,57)(19,56)(20,60)(21,64)(22,63)(23,62)(24,61)(25,75)
(26,79)(27,78)(28,77)(29,76)(30,80)(31,84)(32,83)(33,82)(34,81)(35,65)(36,69)
(37,68)(38,67)(39,66)(40,70)(41,74)(42,73)(43,72)(44,71);;
s4 := ( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,41)(26,40)
(27,44)(28,43)(29,42)(30,36)(31,35)(32,39)(33,38)(34,37)(45,46)(47,49)(50,51)
(52,54)(55,56)(57,59)(60,61)(62,64)(65,81)(66,80)(67,84)(68,83)(69,82)(70,76)
(71,75)(72,79)(73,78)(74,77);;
s5 := ( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)(14,34)
(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)(24,44)(45,75)
(46,76)(47,77)(48,78)(49,79)(50,80)(51,81)(52,82)(53,83)(54,84)(55,65)(56,66)
(57,67)(58,68)(59,69)(60,70)(61,71)(62,72)(63,73)(64,74);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5,
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(84)!(1,2);
s1 := Sym(84)!(3,4);
s2 := Sym(84)!(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)
(54,64)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83)(74,84);
s3 := Sym(84)!( 5,45)( 6,49)( 7,48)( 8,47)( 9,46)(10,50)(11,54)(12,53)(13,52)
(14,51)(15,55)(16,59)(17,58)(18,57)(19,56)(20,60)(21,64)(22,63)(23,62)(24,61)
(25,75)(26,79)(27,78)(28,77)(29,76)(30,80)(31,84)(32,83)(33,82)(34,81)(35,65)
(36,69)(37,68)(38,67)(39,66)(40,70)(41,74)(42,73)(43,72)(44,71);
s4 := Sym(84)!( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,41)
(26,40)(27,44)(28,43)(29,42)(30,36)(31,35)(32,39)(33,38)(34,37)(45,46)(47,49)
(50,51)(52,54)(55,56)(57,59)(60,61)(62,64)(65,81)(66,80)(67,84)(68,83)(69,82)
(70,76)(71,75)(72,79)(73,78)(74,77);
s5 := Sym(84)!( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)
(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)(24,44)
(45,75)(46,76)(47,77)(48,78)(49,79)(50,80)(51,81)(52,82)(53,83)(54,84)(55,65)
(56,66)(57,67)(58,68)(59,69)(60,70)(61,71)(62,72)(63,73)(64,74);
poly := sub<Sym(84)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope