Polytope of Type {12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4}*192a
if this polytope has a name.
Group : SmallGroup(192,300)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 24, 48, 8
Order of s₀s₁s₂ : 12
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 :
   {12,4,2} of size 384
   {12,4,4} of size 768
   {12,4,6} of size 1152
   {12,4,3} of size 1152
   {12,4,10} of size 1920
Vertex Figure Of :
   {2,12,4} of size 384
   {4,12,4} of size 768
   {4,12,4} of size 768
   {6,12,4} of size 1152
   {6,12,4} of size 1152
   {6,12,4} of size 1152
   {3,12,4} of size 1152
   {6,12,4} of size 1152
   {10,12,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*96a
   3-fold quotients : {4,4}*64
   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 : {24,4}*384a, {12,8}*384a, {12,4}*384a, {24,4}*384b, {12,8}*384b
   3-fold covers : {36,4}*576a, {12,12}*576a, {12,12}*576c
   4-fold covers : {24,8}*768a, {12,8}*768a, {24,8}*768b, {24,4}*768a, {24,8}*768c, {24,8}*768d, {12,16}*768a, {48,4}*768a, {12,16}*768b, {48,4}*768b, {12,4}*768a, {24,4}*768b, {12,8}*768b, {12,8}*768c, {24,8}*768e, {24,4}*768c, {24,4}*768d, {12,8}*768d, {24,8}*768f, {24,8}*768g, {24,8}*768h, {12,4}*768d
   5-fold covers : {12,20}*960a, {60,4}*960a
   6-fold covers : {36,8}*1152a, {72,4}*1152a, {12,24}*1152b, {24,12}*1152a, {24,12}*1152b, {12,24}*1152c, {36,4}*1152a, {72,4}*1152b, {36,8}*1152b, {12,12}*1152a, {12,24}*1152d, {12,24}*1152e, {24,12}*1152e, {12,12}*1152c, {24,12}*1152f
   7-fold covers : {12,28}*1344a, {84,4}*1344a
   9-fold covers : {108,4}*1728a, {12,36}*1728a, {36,12}*1728a, {36,12}*1728b, {12,12}*1728a, {12,12}*1728c, {12,12}*1728h, {12,4}*1728c, {12,4}*1728d, {12,12}*1728s
   10-fold covers : {60,8}*1920a, {120,4}*1920a, {12,40}*1920a, {24,20}*1920a, {60,4}*1920a, {120,4}*1920b, {60,8}*1920b, {12,40}*1920b, {24,20}*1920b, {12,20}*1920a
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, 8)(10,11)(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)( 7,19)( 8,20)( 9,21)(10,22)
(11,23)(12,24);;
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*s2*s1*s2*s1*s0*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(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, 8)(10,11)(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)( 7,19)( 8,20)( 9,21)
(10,22)(11,23)(12,24);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*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