Polytope of Type {2,6,4,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4,12}*1152
if this polytope has a name.
Group : SmallGroup(1152,134264)
Rank : 5
Schlafli Type : {2,6,4,12}
Number of vertices, edges, etc : 2, 6, 12, 24, 12
Order of s0s1s2s3s4 : 12
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 : {2,6,2,12}*576, {2,6,4,6}*576
3-fold quotients : {2,2,4,12}*384a, {2,6,4,4}*384
4-fold quotients : {2,3,2,12}*288, {2,6,2,6}*288
6-fold quotients : {2,2,2,12}*192, {2,2,4,6}*192a, {2,6,2,4}*192, {2,6,4,2}*192a
8-fold quotients : {2,3,2,6}*144, {2,6,2,3}*144
9-fold quotients : {2,2,4,4}*128
12-fold quotients : {2,3,2,4}*96, {2,2,2,6}*96, {2,6,2,2}*96
16-fold quotients : {2,3,2,3}*72
18-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
24-fold quotients : {2,2,2,3}*48, {2,3,2,2}*48
36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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);;
s2 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,34)(36,37)(39,49)(40,48)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)(47,56)
(57,67)(58,66)(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74);;
s3 := ( 3,39)( 4,40)( 5,41)( 6,45)( 7,46)( 8,47)( 9,42)(10,43)(11,44)(12,48)
(13,49)(14,50)(15,54)(16,55)(17,56)(18,51)(19,52)(20,53)(21,57)(22,58)(23,59)
(24,63)(25,64)(26,65)(27,60)(28,61)(29,62)(30,66)(31,67)(32,68)(33,72)(34,73)
(35,74)(36,69)(37,70)(38,71);;
s4 := ( 3, 6)( 4, 7)( 5, 8)(12,15)(13,16)(14,17)(21,24)(22,25)(23,26)(30,33)
(31,34)(32,35)(39,60)(40,61)(41,62)(42,57)(43,58)(44,59)(45,63)(46,64)(47,65)
(48,69)(49,70)(50,71)(51,66)(52,67)(53,68)(54,72)(55,73)(56,74);;
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*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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := 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)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)
(64,65)(67,68)(70,71)(73,74);
s2 := Sym(74)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)
(30,31)(33,34)(36,37)(39,49)(40,48)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)
(47,56)(57,67)(58,66)(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74);
s3 := Sym(74)!( 3,39)( 4,40)( 5,41)( 6,45)( 7,46)( 8,47)( 9,42)(10,43)(11,44)
(12,48)(13,49)(14,50)(15,54)(16,55)(17,56)(18,51)(19,52)(20,53)(21,57)(22,58)
(23,59)(24,63)(25,64)(26,65)(27,60)(28,61)(29,62)(30,66)(31,67)(32,68)(33,72)
(34,73)(35,74)(36,69)(37,70)(38,71);
s4 := Sym(74)!( 3, 6)( 4, 7)( 5, 8)(12,15)(13,16)(14,17)(21,24)(22,25)(23,26)
(30,33)(31,34)(32,35)(39,60)(40,61)(41,62)(42,57)(43,58)(44,59)(45,63)(46,64)
(47,65)(48,69)(49,70)(50,71)(51,66)(52,67)(53,68)(54,72)(55,73)(56,74);
poly := sub<Sym(74)|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*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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope