Polytope of Type {2,4,4,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,6,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,134263)
Rank : 6
Schlafli Type : {2,4,4,6,3}
Number of vertices, edges, etc : 2, 4, 8, 12, 9, 3
Order of s0s1s2s3s4s5 : 12
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 : {2,4,2,6,3}*576, {2,2,4,6,3}*576
3-fold quotients : {2,4,4,2,3}*384
4-fold quotients : {2,2,2,6,3}*288
6-fold quotients : {2,2,4,2,3}*192, {2,4,2,2,3}*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 := (39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(57,66)
(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74);;
s2 := ( 3,39)( 4,40)( 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)(23,59)
(24,60)(25,61)(26,62)(27,63)(28,64)(29,65)(30,66)(31,67)(32,68)(33,69)(34,70)
(35,71)(36,72)(37,73)(38,74);;
s3 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(39,57)(40,59)(41,58)(42,60)(43,62)(44,61)(45,63)(46,65)(47,64)
(48,66)(49,68)(50,67)(51,69)(52,71)(53,70)(54,72)(55,74)(56,73);;
s4 := ( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,22)(24,28)
(25,27)(26,29)(30,31)(33,37)(34,36)(35,38)(39,40)(42,46)(43,45)(44,47)(48,49)
(51,55)(52,54)(53,56)(57,58)(60,64)(61,63)(62,65)(66,67)(69,73)(70,72)
(71,74);;
s5 := ( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)(22,26)
(23,25)(28,29)(30,33)(31,35)(32,34)(37,38)(39,42)(40,44)(41,43)(46,47)(48,51)
(49,53)(50,52)(55,56)(57,60)(58,62)(59,61)(64,65)(66,69)(67,71)(68,70)
(73,74);;
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, 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,
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*s4*s3*s2*s3*s4*s3,
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := Sym(74)!(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)
(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74);
s2 := Sym(74)!( 3,39)( 4,40)( 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)
(23,59)(24,60)(25,61)(26,62)(27,63)(28,64)(29,65)(30,66)(31,67)(32,68)(33,69)
(34,70)(35,71)(36,72)(37,73)(38,74);
s3 := Sym(74)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(39,57)(40,59)(41,58)(42,60)(43,62)(44,61)(45,63)(46,65)
(47,64)(48,66)(49,68)(50,67)(51,69)(52,71)(53,70)(54,72)(55,74)(56,73);
s4 := Sym(74)!( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,22)
(24,28)(25,27)(26,29)(30,31)(33,37)(34,36)(35,38)(39,40)(42,46)(43,45)(44,47)
(48,49)(51,55)(52,54)(53,56)(57,58)(60,64)(61,63)(62,65)(66,67)(69,73)(70,72)
(71,74);
s5 := Sym(74)!( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)
(22,26)(23,25)(28,29)(30,33)(31,35)(32,34)(37,38)(39,42)(40,44)(41,43)(46,47)
(48,51)(49,53)(50,52)(55,56)(57,60)(58,62)(59,61)(64,65)(66,69)(67,71)(68,70)
(73,74);
poly := sub<Sym(74)|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,
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, 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*s4*s3*s2*s3*s4*s3, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4 >;
to this polytope