Polytope of Type {3,2,24,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,24,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,33799)
Rank : 5
Schlafli Type : {3,2,24,6}
Number of vertices, edges, etc : 3, 3, 24, 72, 6
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 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 : {3,2,12,6}*864a
3-fold quotients : {3,2,24,2}*576, {3,2,8,6}*576
4-fold quotients : {3,2,6,6}*432a
6-fold quotients : {3,2,12,2}*288, {3,2,4,6}*288a
9-fold quotients : {3,2,8,2}*192
12-fold quotients : {3,2,2,6}*144, {3,2,6,2}*144
18-fold quotients : {3,2,4,2}*96
24-fold quotients : {3,2,2,3}*72, {3,2,3,2}*72
36-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(22,31)(23,32)(24,33)(25,37)
(26,38)(27,39)(28,34)(29,35)(30,36)(40,58)(41,59)(42,60)(43,64)(44,65)(45,66)
(46,61)(47,62)(48,63)(49,67)(50,68)(51,69)(52,73)(53,74)(54,75)(55,70)(56,71)
(57,72);;
s3 := ( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)(11,48)(12,47)(13,52)
(14,54)(15,53)(16,49)(17,51)(18,50)(19,55)(20,57)(21,56)(22,70)(23,72)(24,71)
(25,67)(26,69)(27,68)(28,73)(29,75)(30,74)(31,61)(32,63)(33,62)(34,58)(35,60)
(36,59)(37,64)(38,66)(39,65);;
s4 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)
(67,68)(70,71)(73,74);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(75)!(2,3);
s1 := Sym(75)!(1,2);
s2 := Sym(75)!( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(22,31)(23,32)(24,33)
(25,37)(26,38)(27,39)(28,34)(29,35)(30,36)(40,58)(41,59)(42,60)(43,64)(44,65)
(45,66)(46,61)(47,62)(48,63)(49,67)(50,68)(51,69)(52,73)(53,74)(54,75)(55,70)
(56,71)(57,72);
s3 := Sym(75)!( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)(11,48)(12,47)
(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,55)(20,57)(21,56)(22,70)(23,72)
(24,71)(25,67)(26,69)(27,68)(28,73)(29,75)(30,74)(31,61)(32,63)(33,62)(34,58)
(35,60)(36,59)(37,64)(38,66)(39,65);
s4 := Sym(75)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)
(64,65)(67,68)(70,71)(73,74);
poly := sub<Sym(75)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, 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*s1*s0*s1*s0*s1,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope