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