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# Polytope of Type {4,12,2}

Atlas Canonical Name : {4,12,2}*192c
if this polytope has a name.
Group : SmallGroup(192,1470)
Rank : 4
Schlafli Type : {4,12,2}
Number of vertices, edges, etc : 4, 24, 12, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,12,2,2} of size 384
{4,12,2,3} of size 576
{4,12,2,4} of size 768
{4,12,2,5} of size 960
{4,12,2,6} of size 1152
{4,12,2,7} of size 1344
{4,12,2,9} of size 1728
{4,12,2,10} of size 1920
Vertex Figure Of :
{2,4,12,2} of size 384
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6,2}*96c
4-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,4}*384e, {4,12,2}*384b
3-fold covers : {4,36,2}*576c, {4,12,6}*576f, {4,12,6}*576g
4-fold covers : {4,12,2}*768c, {4,12,8}*768d, {4,12,4}*768f, {4,12,2}*768d, {8,12,2}*768e, {8,12,2}*768f, {4,24,2}*768c, {4,24,2}*768d, {4,12,4}*768n
5-fold covers : {4,12,10}*960c, {4,60,2}*960c
6-fold covers : {4,36,4}*1152e, {4,36,2}*1152b, {4,12,12}*1152f, {4,12,12}*1152g, {4,12,6}*1152e, {4,12,6}*1152f, {12,12,2}*1152f, {12,12,2}*1152g
7-fold covers : {4,12,14}*1344c, {4,84,2}*1344c
9-fold covers : {4,108,2}*1728c, {4,12,18}*1728d, {4,36,6}*1728e, {4,36,6}*1728f, {4,12,6}*1728f, {4,12,6}*1728g, {4,12,6}*1728m, {12,12,2}*1728o
10-fold covers : {4,12,20}*1920c, {4,60,4}*1920e, {4,12,10}*1920b, {20,12,2}*1920b, {4,60,2}*1920b
Permutation Representation (GAP) :
s0 := ( 1,21)( 2,13)( 3,10)( 4,35)( 5,36)( 6, 7)( 8,27)( 9,28)(11,22)(12,23)
(14,19)(15,20)(16,47)(17,48)(18,46)(24,42)(25,44)(26,40)(29,45)(30,43)(31,41)
(32,39)(33,37)(34,38);;
s1 := ( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)
(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)
(42,45);;
s2 := ( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)(14,22)
(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)(33,41)
(38,44)(40,47)(45,46);;
s3 := (49,50);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(50)!( 1,21)( 2,13)( 3,10)( 4,35)( 5,36)( 6, 7)( 8,27)( 9,28)(11,22)
(12,23)(14,19)(15,20)(16,47)(17,48)(18,46)(24,42)(25,44)(26,40)(29,45)(30,43)
(31,41)(32,39)(33,37)(34,38);
s1 := Sym(50)!( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)
(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)
(39,48)(42,45);
s2 := Sym(50)!( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)
(14,22)(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)
(33,41)(38,44)(40,47)(45,46);
s3 := Sym(50)!(49,50);
poly := sub<Sym(50)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 >;

to this polytope