Polytope of Type {4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 3
Schlafli Type : {4,6}
Number of vertices, edges, etc : 8, 24, 12
Order of s0s1s2 : 6
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{4,6,2} of size 192
{4,6,3} of size 384
{4,6,3} of size 384
{4,6,4} of size 384
{4,6,4} of size 384
{4,6,4} of size 384
{4,6,6} of size 576
{4,6,6} of size 576
{4,6,3} of size 768
{4,6,6} of size 768
{4,6,6} of size 768
{4,6,6} of size 768
{4,6,6} of size 768
{4,6,8} of size 768
{4,6,4} of size 768
{4,6,4} of size 768
{4,6,6} of size 864
{4,6,10} of size 960
{4,6,3} of size 1152
{4,6,12} of size 1152
{4,6,12} of size 1152
{4,6,12} of size 1152
{4,6,14} of size 1344
{4,6,18} of size 1728
{4,6,6} of size 1728
{4,6,6} of size 1728
{4,6,6} of size 1728
{4,6,15} of size 1920
{4,6,20} of size 1920
{4,6,20} of size 1920
{4,6,4} of size 1920
Vertex Figure Of :
{2,4,6} of size 192
{4,4,6} of size 384
{6,4,6} of size 576
{4,4,6} of size 768
{4,4,6} of size 768
{8,4,6} of size 768
{10,4,6} of size 960
{3,4,6} of size 1152
{12,4,6} of size 1152
{3,4,6} of size 1152
{14,4,6} of size 1344
{4,4,6} of size 1440
{4,4,6} of size 1440
{18,4,6} of size 1728
{20,4,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
4-fold quotients : {4,3}*24, {2,6}*24
8-fold quotients : {2,3}*12
12-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12}*192b, {4,6}*192b, {4,12}*192c, {8,6}*192b, {8,6}*192c
3-fold covers : {4,18}*288, {12,6}*288a, {12,6}*288b
4-fold covers : {4,12}*384d, {8,12}*384e, {8,12}*384f, {4,6}*384a, {8,6}*384d, {8,6}*384e, {8,6}*384f, {8,12}*384g, {8,12}*384h, {4,24}*384c, {4,24}*384d, {8,6}*384g, {4,12}*384e, {4,24}*384e, {4,6}*384b, {4,24}*384f
5-fold covers : {20,6}*480c, {4,30}*480
6-fold covers : {4,36}*576b, {4,18}*576b, {4,36}*576c, {8,18}*576b, {8,18}*576c, {12,12}*576f, {12,12}*576g, {12,6}*576b, {12,12}*576i, {24,6}*576b, {24,6}*576c, {24,6}*576d, {24,6}*576e, {12,6}*576f, {12,12}*576k
7-fold covers : {28,6}*672, {4,42}*672
8-fold covers : {8,6}*768d, {8,12}*768k, {8,6}*768e, {8,6}*768f, {8,12}*768l, {8,6}*768g, {8,6}*768h, {8,6}*768i, {8,12}*768m, {8,12}*768n, {8,24}*768i, {8,24}*768j, {8,24}*768k, {8,24}*768l, {8,6}*768j, {8,24}*768m, {8,12}*768o, {8,24}*768n, {8,12}*768p, {8,24}*768o, {8,24}*768p, {4,12}*768b, {4,6}*768a, {4,12}*768c, {8,12}*768q, {8,12}*768r, {8,12}*768s, {4,24}*768i, {4,12}*768d, {8,12}*768t, {4,24}*768j, {8,12}*768u, {4,12}*768e, {4,24}*768k, {8,6}*768k, {8,12}*768v, {8,12}*768w, {4,12}*768f, {4,24}*768l, {8,6}*768l, {8,12}*768x, {8,6}*768m, {8,6}*768n, {4,6}*768b, {4,6}*768c, {4,12}*768g, {4,12}*768h, {4,48}*768c, {4,48}*768d, {16,6}*768b, {16,6}*768c
9-fold covers : {4,54}*864, {36,6}*864, {12,18}*864a, {12,18}*864b, {12,6}*864a, {12,6}*864b, {12,6}*864c
10-fold covers : {20,12}*960b, {20,6}*960e, {40,6}*960d, {40,6}*960e, {20,12}*960c, {4,60}*960b, {4,30}*960b, {4,60}*960c, {8,30}*960b, {8,30}*960c
11-fold covers : {44,6}*1056, {4,66}*1056
12-fold covers : {4,36}*1152d, {8,36}*1152e, {8,36}*1152f, {4,18}*1152a, {8,18}*1152d, {8,18}*1152e, {8,18}*1152f, {8,36}*1152g, {8,36}*1152h, {4,72}*1152c, {4,72}*1152d, {8,18}*1152g, {4,36}*1152e, {4,72}*1152e, {4,18}*1152b, {4,72}*1152f, {24,6}*1152b, {24,6}*1152c, {24,12}*1152i, {24,12}*1152j, {24,12}*1152k, {24,12}*1152l, {24,12}*1152m, {24,6}*1152d, {24,12}*1152n, {12,6}*1152b, {12,6}*1152c, {24,6}*1152e, {24,6}*1152f, {12,24}*1152o, {12,24}*1152p, {12,24}*1152q, {12,24}*1152r, {24,6}*1152h, {12,6}*1152d, {12,24}*1152s, {12,12}*1152i, {12,24}*1152t, {12,12}*1152n, {12,12}*1152o, {24,6}*1152k, {24,6}*1152l, {24,12}*1152u, {24,12}*1152v, {12,12}*1152r, {12,24}*1152w, {12,6}*1152f, {12,24}*1152x, {12,6}*1152j, {12,12}*1152t
13-fold covers : {52,6}*1248, {4,78}*1248
14-fold covers : {28,12}*1344b, {28,6}*1344e, {56,6}*1344b, {56,6}*1344c, {28,12}*1344c, {4,84}*1344b, {4,42}*1344b, {4,84}*1344c, {8,42}*1344b, {8,42}*1344c
15-fold covers : {20,18}*1440, {4,90}*1440, {60,6}*1440c, {12,30}*1440a, {12,30}*1440b, {60,6}*1440d
17-fold covers : {68,6}*1632, {4,102}*1632
18-fold covers : {4,108}*1728b, {4,54}*1728b, {4,108}*1728c, {8,54}*1728b, {8,54}*1728c, {36,12}*1728c, {36,6}*1728b, {72,6}*1728b, {72,6}*1728c, {36,12}*1728d, {12,36}*1728e, {12,36}*1728f, {12,18}*1728c, {12,36}*1728g, {12,12}*1728k, {12,12}*1728l, {12,6}*1728b, {12,12}*1728n, {24,18}*1728b, {24,18}*1728c, {24,18}*1728d, {24,6}*1728b, {24,6}*1728c, {24,6}*1728d, {24,18}*1728e, {24,6}*1728e, {12,18}*1728d, {12,36}*1728h, {12,6}*1728f, {12,12}*1728p, {24,6}*1728f, {24,6}*1728g, {12,12}*1728w, {12,6}*1728i, {12,12}*1728y, {4,6}*1728, {4,12}*1728e, {12,12}*1728ab
19-fold covers : {76,6}*1824, {4,114}*1824
20-fold covers : {40,6}*1920a, {40,12}*1920e, {40,12}*1920f, {40,6}*1920b, {20,6}*1920a, {40,6}*1920c, {20,24}*1920c, {20,24}*1920d, {40,6}*1920d, {20,6}*1920b, {20,12}*1920b, {20,12}*1920c, {40,12}*1920g, {40,12}*1920h, {20,24}*1920e, {20,24}*1920f, {4,60}*1920d, {8,60}*1920e, {8,60}*1920f, {4,30}*1920a, {8,30}*1920d, {8,30}*1920e, {8,30}*1920f, {8,60}*1920g, {8,60}*1920h, {4,120}*1920c, {4,120}*1920d, {8,30}*1920g, {4,60}*1920e, {4,120}*1920e, {4,30}*1920b, {4,120}*1920f
Permutation Representation (GAP) :
s0 := ( 1, 6)( 2, 4)( 3,10)( 5, 7)( 8,12)( 9,11)(13,16)(14,15);;
s1 := ( 4, 8)( 6,11)( 7,13)(10,15);;
s2 := ( 1, 3)( 2, 5)( 4, 7)( 6,10)( 8,14)( 9,13)(11,16)(12,15);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(16)!( 1, 6)( 2, 4)( 3,10)( 5, 7)( 8,12)( 9,11)(13,16)(14,15);
s1 := Sym(16)!( 4, 8)( 6,11)( 7,13)(10,15);
s2 := Sym(16)!( 1, 3)( 2, 5)( 4, 7)( 6,10)( 8,14)( 9,13)(11,16)(12,15);
poly := sub<Sym(16)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope