Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*192b
if this polytope has a name.
Group : SmallGroup(192,381)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 12, 48, 8
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,8,2} of size 384
   {12,8,4} of size 768
   {12,8,4} of size 768
   {12,8,6} of size 1152
   {12,8,10} of size 1920
Vertex Figure Of :
   {2,12,8} of size 384
   {4,12,8} of size 768
   {4,12,8} of size 768
   {6,12,8} of size 1152
   {6,12,8} of size 1152
   {6,12,8} of size 1152
   {10,12,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*96a
   3-fold quotients : {4,8}*64b
   4-fold quotients : {12,2}*48, {6,4}*48a
   6-fold quotients : {4,4}*32
   8-fold quotients : {6,2}*24
   12-fold quotients : {2,4}*16, {4,2}*16
   16-fold quotients : {3,2}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,8}*384a, {12,8}*384a, {24,8}*384c
   3-fold covers : {36,8}*576b, {12,24}*576a, {12,24}*576e
   4-fold covers : {24,8}*768a, {12,8}*768a, {24,8}*768c, {12,16}*768a, {12,16}*768b, {24,16}*768a, {24,16}*768b, {48,8}*768c, {48,8}*768e, {12,8}*768w
   5-fold covers : {12,40}*960b, {60,8}*960b
   6-fold covers : {36,8}*1152a, {12,24}*1152b, {12,24}*1152c, {72,8}*1152b, {24,24}*1152c, {24,24}*1152g, {72,8}*1152d, {24,24}*1152k, {24,24}*1152l
   7-fold covers : {12,56}*1344b, {84,8}*1344b
   9-fold covers : {108,8}*1728b, {36,24}*1728a, {12,24}*1728a, {12,72}*1728c, {36,24}*1728d, {12,24}*1728f, {12,24}*1728p, {12,8}*1728f, {12,8}*1728h, {12,24}*1728w
   10-fold covers : {60,8}*1920a, {12,40}*1920a, {120,8}*1920b, {24,40}*1920b, {120,8}*1920d, {24,40}*1920d
Permutation Representation (GAP) :

s0 := ( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(14,15)(17,18)(19,22)(20,24)(21,23);;
s1 := ( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,20)(14,19)(15,21)(16,23)(17,22)
(18,24);;
s2 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5,17)( 6,18)( 7,22)( 8,23)( 9,24)(10,19)
(11,20)(12,21);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(24)!( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(14,15)(17,18)(19,22)(20,24)
(21,23);
s1 := Sym(24)!( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,20)(14,19)(15,21)(16,23)
(17,22)(18,24);
s2 := Sym(24)!( 1,13)( 2,14)( 3,15)( 4,16)( 5,17)( 6,18)( 7,22)( 8,23)( 9,24)
(10,19)(11,20)(12,21);
poly := sub<Sym(24)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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*s0*s1 >;

References : None.
to this polytope