Polytope of Type {6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3}*48
Also Known As : {6,3}(2,0), {6,3}4. if this polytope has another name.
Group : SmallGroup(48,48)
Rank : 3
Schlafli Type : {6,3}
Number of vertices, edges, etc : 8, 12, 4
Order of s0s1s2 : 4
Order of s0s1s2s1 : 6
Special Properties :
Toroidal
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{6,3,2} of size 96
{6,3,3} of size 240
{6,3,4} of size 384
{6,3,4} of size 384
{6,3,6} of size 480
{6,3,4} of size 768
{6,3,6} of size 1440
Vertex Figure Of :
{2,6,3} of size 96
{4,6,3} of size 192
{3,6,3} of size 240
{6,6,3} of size 288
{4,6,3} of size 384
{4,6,3} of size 384
{8,6,3} of size 384
{6,6,3} of size 480
{10,6,3} of size 480
{12,6,3} of size 576
{14,6,3} of size 672
{4,6,3} of size 720
{3,6,3} of size 720
{4,6,3} of size 768
{4,6,3} of size 768
{4,6,3} of size 768
{16,6,3} of size 768
{18,6,3} of size 864
{12,6,3} of size 960
{20,6,3} of size 960
{22,6,3} of size 1056
{12,6,3} of size 1152
{24,6,3} of size 1152
{15,6,3} of size 1200
{26,6,3} of size 1248
{6,6,3} of size 1296
{28,6,3} of size 1344
{4,6,3} of size 1440
{4,6,3} of size 1440
{4,6,3} of size 1440
{6,6,3} of size 1440
{6,6,3} of size 1440
{30,6,3} of size 1440
{34,6,3} of size 1632
{21,6,3} of size 1680
{36,6,3} of size 1728
{38,6,3} of size 1824
{20,6,3} of size 1920
{40,6,3} of size 1920
{24,6,3} of size 1920
{6,6,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,3}*96, {6,6}*96
3-fold covers : {6,3}*144
4-fold covers : {6,3}*192, {6,12}*192a, {12,6}*192a, {6,12}*192b, {12,6}*192b, {6,6}*192b
5-fold covers : {6,15}*240
6-fold covers : {12,3}*288, {6,6}*288a, {6,6}*288b
7-fold covers : {6,21}*336
8-fold covers : {12,3}*384, {12,12}*384a, {12,12}*384b, {6,6}*384c, {6,6}*384d, {6,6}*384e, {6,12}*384, {12,6}*384, {12,12}*384c, {12,12}*384d, {6,24}*384a, {24,6}*384a, {6,24}*384b, {24,6}*384b
9-fold covers : {6,9}*432, {6,3}*432
10-fold covers : {12,15}*480, {6,30}*480, {30,6}*480
11-fold covers : {6,33}*528
12-fold covers : {6,3}*576, {6,12}*576a, {12,6}*576a, {6,12}*576c, {12,6}*576c, {6,6}*576a, {6,6}*576b, {6,12}*576d, {12,6}*576d, {6,12}*576e, {12,6}*576e, {12,3}*576
13-fold covers : {6,39}*624
14-fold covers : {12,21}*672, {6,42}*672, {42,6}*672
15-fold covers : {6,15}*720e
16-fold covers : {24,3}*768, {6,3}*768, {6,12}*768c, {12,6}*768c, {6,12}*768d, {12,6}*768d, {6,12}*768e, {12,6}*768e, {6,6}*768b, {6,6}*768c, {6,6}*768d, {6,24}*768, {24,6}*768, {12,24}*768a, {24,12}*768a, {12,24}*768b, {24,12}*768b, {6,12}*768f, {12,6}*768f, {12,12}*768a, {12,12}*768b, {12,12}*768c, {12,24}*768c, {24,12}*768c, {12,24}*768d, {24,12}*768d, {6,12}*768g, {12,6}*768g, {12,24}*768e, {24,12}*768e, {12,24}*768f, {24,12}*768f, {6,12}*768h, {12,6}*768h, {6,6}*768e, {6,12}*768i, {12,6}*768i, {6,6}*768f, {6,12}*768j, {12,6}*768j, {6,48}*768a, {48,6}*768a, {6,48}*768b, {48,6}*768b
17-fold covers : {6,51}*816
18-fold covers : {12,9}*864, {12,3}*864, {6,18}*864, {18,6}*864, {6,6}*864a, {6,6}*864b, {6,6}*864c
19-fold covers : {6,57}*912
20-fold covers : {6,15}*960, {6,60}*960a, {60,6}*960a, {12,30}*960a, {30,12}*960a, {6,30}*960, {30,6}*960, {6,60}*960b, {60,6}*960b, {12,30}*960b, {30,12}*960b
21-fold covers : {6,21}*1008b
22-fold covers : {12,33}*1056, {6,66}*1056, {66,6}*1056
23-fold covers : {6,69}*1104
24-fold covers : {12,3}*1152a, {6,6}*1152a, {6,6}*1152b, {12,12}*1152d, {12,12}*1152e, {12,12}*1152f, {12,12}*1152g, {6,12}*1152a, {12,6}*1152a, {6,6}*1152c, {6,6}*1152d, {6,6}*1152e, {6,6}*1152f, {6,24}*1152g, {24,6}*1152g, {6,24}*1152i, {24,6}*1152i, {12,12}*1152j, {12,12}*1152l, {6,24}*1152j, {24,6}*1152j, {6,12}*1152e, {12,6}*1152e, {12,12}*1152p, {12,12}*1152q, {6,24}*1152m, {24,6}*1152m, {12,3}*1152b, {12,6}*1152g, {24,3}*1152b, {24,3}*1152c, {6,12}*1152j, {12,6}*1152j
25-fold covers : {6,75}*1200, {30,15}*1200, {6,3}*1200
26-fold covers : {12,39}*1248, {6,78}*1248, {78,6}*1248
27-fold covers : {6,27}*1296, {18,9}*1296a, {6,9}*1296a, {6,3}*1296, {6,9}*1296b, {18,3}*1296a, {6,9}*1296c, {6,9}*1296d, {6,9}*1296e, {6,9}*1296f, {18,3}*1296b, {18,9}*1296b, {18,9}*1296c
28-fold covers : {6,21}*1344, {6,84}*1344a, {84,6}*1344a, {12,42}*1344a, {42,12}*1344a, {6,42}*1344, {42,6}*1344, {6,84}*1344b, {84,6}*1344b, {12,42}*1344b, {42,12}*1344b
29-fold covers : {6,87}*1392
30-fold covers : {12,15}*1440c, {6,30}*1440g, {30,6}*1440g, {6,30}*1440h, {30,6}*1440h
31-fold covers : {6,93}*1488
33-fold covers : {6,33}*1584
34-fold covers : {12,51}*1632, {6,102}*1632, {102,6}*1632
35-fold covers : {6,105}*1680
36-fold covers : {6,9}*1728, {6,3}*1728, {6,36}*1728a, {36,6}*1728a, {12,18}*1728a, {18,12}*1728a, {6,18}*1728a, {18,6}*1728a, {6,36}*1728c, {36,6}*1728c, {12,18}*1728b, {18,12}*1728b, {6,12}*1728a, {12,6}*1728a, {6,12}*1728c, {12,6}*1728c, {6,6}*1728a, {6,6}*1728b, {6,12}*1728d, {12,6}*1728d, {6,12}*1728e, {12,6}*1728e, {12,9}*1728, {12,3}*1728, {6,12}*1728g, {12,6}*1728g, {6,6}*1728f, {6,12}*1728h, {12,6}*1728h, {6,12}*1728j, {12,6}*1728j, {12,12}*1728z
37-fold covers : {6,111}*1776
38-fold covers : {12,57}*1824, {6,114}*1824, {114,6}*1824
39-fold covers : {6,39}*1872
40-fold covers : {12,15}*1920, {6,30}*1920a, {30,6}*1920a, {12,60}*1920a, {60,12}*1920a, {12,60}*1920b, {60,12}*1920b, {6,60}*1920, {60,6}*1920, {6,30}*1920b, {30,6}*1920b, {6,30}*1920c, {30,6}*1920c, {6,120}*1920a, {120,6}*1920a, {6,120}*1920b, {120,6}*1920b, {12,60}*1920c, {60,12}*1920c, {24,30}*1920a, {30,24}*1920a, {12,30}*1920, {30,12}*1920, {12,60}*1920d, {60,12}*1920d, {24,30}*1920b, {30,24}*1920b
41-fold covers : {6,123}*1968
Permutation Representation (GAP) :
s0 := (1,4)(2,6);;
s1 := (1,2)(3,4)(5,6);;
s2 := (1,4)(2,6)(3,5);;
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,
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(6)!(1,4)(2,6);
s1 := Sym(6)!(1,2)(3,4)(5,6);
s2 := Sym(6)!(1,4)(2,6)(3,5);
poly := sub<Sym(6)|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, s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope