Polytope of Type {2,8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,12}*384a
if this polytope has a name.
Group : SmallGroup(384,11319)
Rank : 4
Schlafli Type : {2,8,12}
Number of vertices, edges, etc : 2, 8, 48, 12
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,8,12,2} of size 768
Vertex Figure Of :
{2,2,8,12} of size 768
{3,2,8,12} of size 1152
{5,2,8,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,12}*192a, {2,8,6}*192
3-fold quotients : {2,8,4}*128a
4-fold quotients : {2,2,12}*96, {2,4,6}*96a
6-fold quotients : {2,4,4}*64, {2,8,2}*64
8-fold quotients : {2,2,6}*48
12-fold quotients : {2,2,4}*32, {2,4,2}*32
16-fold quotients : {2,2,3}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,8,12}*768a, {2,8,24}*768a, {2,8,24}*768c, {4,8,12}*768d, {2,16,12}*768a, {2,16,12}*768b
3-fold covers : {2,8,36}*1152a, {6,8,12}*1152a, {2,24,12}*1152a, {2,24,12}*1152c
5-fold covers : {2,8,60}*1920a, {10,8,12}*1920a, {2,40,12}*1920a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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);;
s2 := ( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,36)(10,38)(11,37)(12,33)
(13,35)(14,34)(15,39)(16,41)(17,40)(18,42)(19,44)(20,43)(21,48)(22,50)(23,49)
(24,45)(25,47)(26,46)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)(57,84)(58,86)
(59,85)(60,81)(61,83)(62,82)(63,87)(64,89)(65,88)(66,90)(67,92)(68,91)(69,96)
(70,98)(71,97)(72,93)(73,95)(74,94);;
s3 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,40)(28,39)
(29,41)(30,43)(31,42)(32,44)(33,46)(34,45)(35,47)(36,49)(37,48)(38,50)(51,52)
(54,55)(57,58)(60,61)(63,64)(66,67)(69,70)(72,73)(75,88)(76,87)(77,89)(78,91)
(79,90)(80,92)(81,94)(82,93)(83,95)(84,97)(85,96)(86,98);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := 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);
s2 := Sym(98)!( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,36)(10,38)(11,37)
(12,33)(13,35)(14,34)(15,39)(16,41)(17,40)(18,42)(19,44)(20,43)(21,48)(22,50)
(23,49)(24,45)(25,47)(26,46)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)(57,84)
(58,86)(59,85)(60,81)(61,83)(62,82)(63,87)(64,89)(65,88)(66,90)(67,92)(68,91)
(69,96)(70,98)(71,97)(72,93)(73,95)(74,94);
s3 := Sym(98)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,40)
(28,39)(29,41)(30,43)(31,42)(32,44)(33,46)(34,45)(35,47)(36,49)(37,48)(38,50)
(51,52)(54,55)(57,58)(60,61)(63,64)(66,67)(69,70)(72,73)(75,88)(76,87)(77,89)
(78,91)(79,90)(80,92)(81,94)(82,93)(83,95)(84,97)(85,96)(86,98);
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope