Polytope of Type {2,2,8,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,8,6,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,152550)
Rank : 6
Schlafli Type : {2,2,8,6,3}
Number of vertices, edges, etc : 2, 2, 8, 24, 9, 3
Order of s0s1s2s3s4s5 : 24
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 : {2,2,4,6,3}*576
3-fold quotients : {2,2,8,2,3}*384
4-fold quotients : {2,2,2,6,3}*288
6-fold quotients : {2,2,4,2,3}*192
12-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,48)(13,49)(14,50)
(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)(23,68)(24,69)(25,70)
(26,71)(27,72)(28,73)(29,74)(30,75)(31,76)(32,59)(33,60)(34,61)(35,62)(36,63)
(37,64)(38,65)(39,66)(40,67);;
s3 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(23,32)(24,33)(25,34)(26,38)
(27,39)(28,40)(29,35)(30,36)(31,37)(41,59)(42,60)(43,61)(44,65)(45,66)(46,67)
(47,62)(48,63)(49,64)(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)(57,72)
(58,73);;
s4 := ( 5, 8)( 6,10)( 7, 9)(12,13)(14,17)(15,19)(16,18)(21,22)(23,26)(24,28)
(25,27)(30,31)(32,35)(33,37)(34,36)(39,40)(41,44)(42,46)(43,45)(48,49)(50,53)
(51,55)(52,54)(57,58)(59,62)(60,64)(61,63)(66,67)(68,71)(69,73)(70,72)
(75,76);;
s5 := ( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)(26,30)
(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,42)(44,48)(45,47)(46,49)(50,51)
(53,57)(54,56)(55,58)(59,60)(62,66)(63,65)(64,67)(68,69)(71,75)(72,74)
(73,76);;
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,
s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3,
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,48)(13,49)
(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)(23,68)(24,69)
(25,70)(26,71)(27,72)(28,73)(29,74)(30,75)(31,76)(32,59)(33,60)(34,61)(35,62)
(36,63)(37,64)(38,65)(39,66)(40,67);
s3 := Sym(76)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(23,32)(24,33)(25,34)
(26,38)(27,39)(28,40)(29,35)(30,36)(31,37)(41,59)(42,60)(43,61)(44,65)(45,66)
(46,67)(47,62)(48,63)(49,64)(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)
(57,72)(58,73);
s4 := Sym(76)!( 5, 8)( 6,10)( 7, 9)(12,13)(14,17)(15,19)(16,18)(21,22)(23,26)
(24,28)(25,27)(30,31)(32,35)(33,37)(34,36)(39,40)(41,44)(42,46)(43,45)(48,49)
(50,53)(51,55)(52,54)(57,58)(59,62)(60,64)(61,63)(66,67)(68,71)(69,73)(70,72)
(75,76);
s5 := Sym(76)!( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)
(26,30)(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,42)(44,48)(45,47)(46,49)
(50,51)(53,57)(54,56)(55,58)(59,60)(62,66)(63,65)(64,67)(68,69)(71,75)(72,74)
(73,76);
poly := sub<Sym(76)|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, s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3,
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope