Polytope of Type {2,2,4,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,4,10}*1280
if this polytope has a name.
Group : SmallGroup(1280,1076197)
Rank : 6
Schlafli Type : {2,2,4,4,10}
Number of vertices, edges, etc : 2, 2, 4, 8, 20, 10
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 : {2,2,2,4,10}*640, {2,2,4,2,10}*640
4-fold quotients : {2,2,4,2,5}*320, {2,2,2,2,10}*320
5-fold quotients : {2,2,4,4,2}*256
8-fold quotients : {2,2,2,2,5}*160
10-fold quotients : {2,2,2,4,2}*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 := (25,30)(26,31)(27,32)(28,33)(29,34)(35,40)(36,41)(37,42)(38,43)(39,44)
(65,70)(66,71)(67,72)(68,73)(69,74)(75,80)(76,81)(77,82)(78,83)(79,84);;
s3 := ( 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)(45,65)
(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)(54,74)(55,75)(56,76)
(57,77)(58,78)(59,79)(60,80)(61,81)(62,82)(63,83)(64,84);;
s4 := ( 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);;
s5 := ( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,26)(27,29)
(30,31)(32,34)(35,36)(37,39)(40,41)(42,44)(45,46)(47,49)(50,51)(52,54)(55,56)
(57,59)(60,61)(62,64)(65,66)(67,69)(70,71)(72,74)(75,76)(77,79)(80,81)
(82,84);;
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*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(84)!(1,2);
s1 := Sym(84)!(3,4);
s2 := Sym(84)!(25,30)(26,31)(27,32)(28,33)(29,34)(35,40)(36,41)(37,42)(38,43)
(39,44)(65,70)(66,71)(67,72)(68,73)(69,74)(75,80)(76,81)(77,82)(78,83)(79,84);
s3 := 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)
(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)(54,74)(55,75)
(56,76)(57,77)(58,78)(59,79)(60,80)(61,81)(62,82)(63,83)(64,84);
s4 := 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);
s5 := Sym(84)!( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,26)
(27,29)(30,31)(32,34)(35,36)(37,39)(40,41)(42,44)(45,46)(47,49)(50,51)(52,54)
(55,56)(57,59)(60,61)(62,64)(65,66)(67,69)(70,71)(72,74)(75,76)(77,79)(80,81)
(82,84);
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*s3*s4*s3*s4*s3*s4,
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;
to this polytope