Polytope of Type {4,6,4,2,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,4,2,5}*1920a
if this polytope has a name.
Group : SmallGroup(1920,208116)
Rank : 6
Schlafli Type : {4,6,4,2,5}
Number of vertices, edges, etc : 4, 12, 12, 4, 5, 5
Order of s0s1s2s3s4s5 : 60
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 : {2,6,4,2,5}*960a, {4,6,2,2,5}*960a
3-fold quotients : {4,2,4,2,5}*640
4-fold quotients : {2,6,2,2,5}*480
6-fold quotients : {2,2,4,2,5}*320, {4,2,2,2,5}*320
8-fold quotients : {2,3,2,2,5}*240
12-fold quotients : {2,2,2,2,5}*160
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)
(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)
(22,70)(23,71)(24,72)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)(32,74)
(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,85)
(44,86)(45,87)(46,88)(47,89)(48,90);;
s1 := ( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)
(11,36)(12,35)(13,43)(14,45)(15,44)(16,46)(17,48)(18,47)(19,37)(20,39)(21,38)
(22,40)(23,42)(24,41)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,79)(56,81)
(57,80)(58,82)(59,84)(60,83)(61,91)(62,93)(63,92)(64,94)(65,96)(66,95)(67,85)
(68,87)(69,86)(70,88)(71,90)(72,89);;
s2 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,23)(14,22)(15,24)(16,20)(17,19)(18,21)
(25,26)(28,29)(31,32)(34,35)(37,47)(38,46)(39,48)(40,44)(41,43)(42,45)(49,50)
(52,53)(55,56)(58,59)(61,71)(62,70)(63,72)(64,68)(65,67)(66,69)(73,74)(76,77)
(79,80)(82,83)(85,95)(86,94)(87,96)(88,92)(89,91)(90,93);;
s3 := ( 1,61)( 2,62)( 3,63)( 4,64)( 5,65)( 6,66)( 7,67)( 8,68)( 9,69)(10,70)
(11,71)(12,72)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)
(22,58)(23,59)(24,60)(25,91)(26,92)(27,93)(28,94)(29,95)(30,96)(31,85)(32,86)
(33,87)(34,88)(35,89)(36,90)(37,79)(38,80)(39,81)(40,82)(41,83)(42,84)(43,73)
(44,74)(45,75)(46,76)(47,77)(48,78);;
s4 := ( 98, 99)(100,101);;
s5 := ( 97, 98)( 99,100);;
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*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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(101)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)
(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)
(21,69)(22,70)(23,71)(24,72)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)
(32,74)(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)
(43,85)(44,86)(45,87)(46,88)(47,89)(48,90);
s1 := Sym(101)!( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)
(10,34)(11,36)(12,35)(13,43)(14,45)(15,44)(16,46)(17,48)(18,47)(19,37)(20,39)
(21,38)(22,40)(23,42)(24,41)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,79)
(56,81)(57,80)(58,82)(59,84)(60,83)(61,91)(62,93)(63,92)(64,94)(65,96)(66,95)
(67,85)(68,87)(69,86)(70,88)(71,90)(72,89);
s2 := Sym(101)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,23)(14,22)(15,24)(16,20)(17,19)
(18,21)(25,26)(28,29)(31,32)(34,35)(37,47)(38,46)(39,48)(40,44)(41,43)(42,45)
(49,50)(52,53)(55,56)(58,59)(61,71)(62,70)(63,72)(64,68)(65,67)(66,69)(73,74)
(76,77)(79,80)(82,83)(85,95)(86,94)(87,96)(88,92)(89,91)(90,93);
s3 := Sym(101)!( 1,61)( 2,62)( 3,63)( 4,64)( 5,65)( 6,66)( 7,67)( 8,68)( 9,69)
(10,70)(11,71)(12,72)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)
(21,57)(22,58)(23,59)(24,60)(25,91)(26,92)(27,93)(28,94)(29,95)(30,96)(31,85)
(32,86)(33,87)(34,88)(35,89)(36,90)(37,79)(38,80)(39,81)(40,82)(41,83)(42,84)
(43,73)(44,74)(45,75)(46,76)(47,77)(48,78);
s4 := Sym(101)!( 98, 99)(100,101);
s5 := Sym(101)!( 97, 98)( 99,100);
poly := sub<Sym(101)|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*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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope