Polytope of Type {12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4}*96b
if this polytope has a name.
Group : SmallGroup(96,187)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 12, 24, 4
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{12,4,2} of size 192
{12,4,4} of size 768
Vertex Figure Of :
{2,12,4} of size 192
{4,12,4} of size 384
{4,12,4} of size 384
{4,12,4} of size 384
{6,12,4} of size 576
{6,12,4} of size 576
{6,12,4} of size 576
{4,12,4} of size 768
{8,12,4} of size 768
{8,12,4} of size 768
{4,12,4} of size 768
{4,12,4} of size 768
{6,12,4} of size 864
{10,12,4} of size 960
{12,12,4} of size 1152
{12,12,4} of size 1152
{6,12,4} of size 1152
{14,12,4} of size 1344
{18,12,4} of size 1728
{6,12,4} of size 1728
{6,12,4} of size 1728
{18,12,4} of size 1728
{6,12,4} of size 1728
{6,12,4} of size 1728
{4,12,4} of size 1728
{6,12,4} of size 1728
{20,12,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,4}*48c
4-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,4}*192c, {24,4}*192d, {12,4}*192b
3-fold covers : {36,4}*288b
4-fold covers : {12,4}*384b, {48,4}*384c, {48,4}*384d, {12,4}*384d, {12,8}*384e, {12,8}*384f, {24,4}*384c, {24,4}*384d
5-fold covers : {60,4}*480b
6-fold covers : {72,4}*576c, {72,4}*576d, {36,4}*576b, {12,12}*576d, {12,12}*576e
7-fold covers : {84,4}*672b
8-fold covers : {24,4}*768e, {24,4}*768f, {12,8}*768e, {12,8}*768f, {96,4}*768c, {96,4}*768d, {24,8}*768i, {24,8}*768j, {24,8}*768k, {24,8}*768l, {12,4}*768b, {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, {12,8}*768w, {12,4}*768f, {24,4}*768l, {48,4}*768c, {48,4}*768d
9-fold covers : {108,4}*864b
10-fold covers : {120,4}*960c, {120,4}*960d, {12,20}*960b, {60,4}*960b
11-fold covers : {132,4}*1056b
12-fold covers : {36,4}*1152b, {144,4}*1152c, {144,4}*1152d, {36,4}*1152d, {36,8}*1152e, {36,8}*1152f, {72,4}*1152c, {72,4}*1152d, {12,24}*1152i, {12,24}*1152j, {12,24}*1152k, {12,24}*1152l, {24,12}*1152o, {24,12}*1152p, {24,12}*1152q, {24,12}*1152r, {12,12}*1152k, {12,12}*1152m
13-fold covers : {156,4}*1248b
14-fold covers : {168,4}*1344c, {168,4}*1344d, {12,28}*1344b, {84,4}*1344b
15-fold covers : {180,4}*1440b
17-fold covers : {204,4}*1632b
18-fold covers : {216,4}*1728c, {216,4}*1728d, {108,4}*1728b, {12,36}*1728c, {36,12}*1728e, {36,12}*1728f, {12,12}*1728i, {12,12}*1728j, {12,12}*1728v, {12,12}*1728aa
19-fold covers : {228,4}*1824b
20-fold covers : {60,4}*1920b, {240,4}*1920c, {240,4}*1920d, {12,40}*1920e, {12,40}*1920f, {24,20}*1920c, {24,20}*1920d, {12,20}*1920c, {60,4}*1920d, {60,8}*1920e, {60,8}*1920f, {120,4}*1920c, {120,4}*1920d
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1, 8)( 2, 4)( 3,19)( 5, 9)( 6,43)( 7,11)(10,34)(12,20)(13,48)(14,42)
(15,26)(16,25)(17,29)(18,23)(21,44)(22,33)(24,38)(27,47)(28,39)(30,37)(31,36)
(32,41)(35,45)(40,46);;
s2 := ( 1,33)( 2,42)( 3,45)( 4,34)( 5,18)( 6,16)( 7,47)( 8,43)( 9,26)(10,29)
(11,44)(12,31)(13,24)(14,17)(15,32)(19,48)(20,39)(21,37)(22,25)(23,41)(27,30)
(28,40)(35,38)(36,46);;
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,
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(48)!( 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);
s1 := Sym(48)!( 1, 8)( 2, 4)( 3,19)( 5, 9)( 6,43)( 7,11)(10,34)(12,20)(13,48)
(14,42)(15,26)(16,25)(17,29)(18,23)(21,44)(22,33)(24,38)(27,47)(28,39)(30,37)
(31,36)(32,41)(35,45)(40,46);
s2 := Sym(48)!( 1,33)( 2,42)( 3,45)( 4,34)( 5,18)( 6,16)( 7,47)( 8,43)( 9,26)
(10,29)(11,44)(12,31)(13,24)(14,17)(15,32)(19,48)(20,39)(21,37)(22,25)(23,41)
(27,30)(28,40)(35,38)(36,46);
poly := sub<Sym(48)|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,
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope