Polytope of Type {3,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,8,2}*192
if this polytope has a name.
Group : SmallGroup(192,1481)
Rank : 4
Schlafli Type : {3,8,2}
Number of vertices, edges, etc : 6, 24, 16, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,8,2,2} of size 384
   {3,8,2,3} of size 576
   {3,8,2,4} of size 768
   {3,8,2,5} of size 960
   {3,8,2,6} of size 1152
   {3,8,2,7} of size 1344
   {3,8,2,9} of size 1728
   {3,8,2,10} of size 1920
Vertex Figure Of :
   {2,3,8,2} of size 384
   {4,3,8,2} of size 768
   {6,3,8,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,4,2}*96
   4-fold quotients : {3,4,2}*48
   8-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,8,4}*384, {6,8,2}*384b
   3-fold covers : {9,8,2}*576, {3,24,2}*576, {3,8,6}*576
   4-fold covers : {3,8,2}*768, {3,8,4}*768a, {3,8,8}*768, {12,8,2}*768e, {6,8,4}*768c, {6,8,2}*768f, {12,8,2}*768h
   5-fold covers : {3,8,10}*960, {15,8,2}*960
   6-fold covers : {9,8,4}*1152, {18,8,2}*1152b, {3,8,12}*1152, {3,24,4}*1152, {6,24,2}*1152b, {6,8,6}*1152b, {6,24,2}*1152e
   7-fold covers : {3,8,14}*1344, {21,8,2}*1344
   9-fold covers : {27,8,2}*1728, {3,8,18}*1728, {9,24,2}*1728, {3,24,2}*1728, {9,8,6}*1728, {3,24,6}*1728a, {3,24,6}*1728b
   10-fold covers : {3,8,20}*1920, {15,8,4}*1920, {6,8,10}*1920a, {6,40,2}*1920c, {30,8,2}*1920b
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)(16,38)
(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)(36,48)
(39,40);;
s1 := ( 1, 4)( 2,13)( 3, 9)( 6,42)( 7,41)( 8,25)(10,14)(11,47)(12,48)(15,40)
(16,39)(17,24)(18,21)(19,20)(22,23)(27,44)(28,46)(29,33)(30,36)(31,32)(34,35)
(37,38);;
s2 := ( 1,44)( 2,40)( 3,39)( 4,47)( 5,33)( 6,34)( 7,31)( 8,46)( 9,42)(10,24)
(11,22)(12,19)(13,41)(14,21)(15,35)(16,32)(17,45)(18,43)(20,27)(23,28)(25,48)
(26,36)(29,38)(30,37);;
s3 := (49,50);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(50)!( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)
(16,38)(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)
(36,48)(39,40);
s1 := Sym(50)!( 1, 4)( 2,13)( 3, 9)( 6,42)( 7,41)( 8,25)(10,14)(11,47)(12,48)
(15,40)(16,39)(17,24)(18,21)(19,20)(22,23)(27,44)(28,46)(29,33)(30,36)(31,32)
(34,35)(37,38);
s2 := Sym(50)!( 1,44)( 2,40)( 3,39)( 4,47)( 5,33)( 6,34)( 7,31)( 8,46)( 9,42)
(10,24)(11,22)(12,19)(13,41)(14,21)(15,35)(16,32)(17,45)(18,43)(20,27)(23,28)
(25,48)(26,36)(29,38)(30,37);
s3 := Sym(50)!(49,50);
poly := sub<Sym(50)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;

to this polytope