Polytope of Type {2,12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,8}*384a
if this polytope has a name.
Group : SmallGroup(384,11319)
Rank : 4
Schlafli Type : {2,12,8}
Number of vertices, edges, etc : 2, 12, 48, 8
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,8,2} of size 768
Vertex Figure Of :
   {2,2,12,8} of size 768
   {3,2,12,8} of size 1152
   {5,2,12,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,4}*192a, {2,6,8}*192
   3-fold quotients : {2,4,8}*128a
   4-fold quotients : {2,12,2}*96, {2,6,4}*96a
   6-fold quotients : {2,4,4}*64, {2,2,8}*64
   8-fold quotients : {2,6,2}*48
   12-fold quotients : {2,2,4}*32, {2,4,2}*32
   16-fold quotients : {2,3,2}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,8}*768a, {2,24,8}*768a, {2,24,8}*768c, {4,12,8}*768a, {2,12,16}*768a, {2,12,16}*768b
   3-fold covers : {2,36,8}*1152a, {6,12,8}*1152a, {6,12,8}*1152b, {2,12,24}*1152a, {2,12,24}*1152c
   5-fold covers : {2,60,8}*1920a, {10,12,8}*1920a, {2,12,40}*1920a
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(27,39)(28,41)
(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)(37,50)(38,49)(52,53)
(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74)(75,87)(76,89)(77,88)(78,90)
(79,92)(80,91)(81,93)(82,95)(83,94)(84,96)(85,98)(86,97);;
s2 := ( 3,28)( 4,27)( 5,29)( 6,31)( 7,30)( 8,32)( 9,37)(10,36)(11,38)(12,34)
(13,33)(14,35)(15,40)(16,39)(17,41)(18,43)(19,42)(20,44)(21,49)(22,48)(23,50)
(24,46)(25,45)(26,47)(51,76)(52,75)(53,77)(54,79)(55,78)(56,80)(57,85)(58,84)
(59,86)(60,82)(61,81)(62,83)(63,88)(64,87)(65,89)(66,91)(67,90)(68,92)(69,97)
(70,96)(71,98)(72,94)(73,93)(74,95);;
s3 := ( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,60)(10,61)(11,62)(12,57)
(13,58)(14,59)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,72)(22,73)(23,74)
(24,69)(25,70)(26,71)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)(34,76)
(35,77)(36,78)(37,79)(38,80)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,87)
(46,88)(47,89)(48,90)(49,91)(50,92);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(27,39)
(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)(37,50)(38,49)
(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74)(75,87)(76,89)(77,88)
(78,90)(79,92)(80,91)(81,93)(82,95)(83,94)(84,96)(85,98)(86,97);
s2 := Sym(98)!( 3,28)( 4,27)( 5,29)( 6,31)( 7,30)( 8,32)( 9,37)(10,36)(11,38)
(12,34)(13,33)(14,35)(15,40)(16,39)(17,41)(18,43)(19,42)(20,44)(21,49)(22,48)
(23,50)(24,46)(25,45)(26,47)(51,76)(52,75)(53,77)(54,79)(55,78)(56,80)(57,85)
(58,84)(59,86)(60,82)(61,81)(62,83)(63,88)(64,87)(65,89)(66,91)(67,90)(68,92)
(69,97)(70,96)(71,98)(72,94)(73,93)(74,95);
s3 := Sym(98)!( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,60)(10,61)(11,62)
(12,57)(13,58)(14,59)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,72)(22,73)
(23,74)(24,69)(25,70)(26,71)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)
(34,76)(35,77)(36,78)(37,79)(38,80)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)
(45,87)(46,88)(47,89)(48,90)(49,91)(50,92);
poly := sub<Sym(98)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope