Polytope of Type {2,12,8,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,8,2}*768a
if this polytope has a name.
Group : SmallGroup(768,1035863)
Rank : 5
Schlafli Type : {2,12,8,2}
Number of vertices, edges, etc : 2, 12, 48, 8, 2
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,12,4,2}*384a, {2,6,8,2}*384
3-fold quotients : {2,4,8,2}*256a
4-fold quotients : {2,12,2,2}*192, {2,6,4,2}*192a
6-fold quotients : {2,4,4,2}*128, {2,2,8,2}*128
8-fold quotients : {2,6,2,2}*96
12-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
16-fold quotients : {2,3,2,2}*48
24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
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);;
s4 := ( 99,100);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, 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(100)!(1,2);
s1 := Sym(100)!( 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(100)!( 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(100)!( 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);
s4 := Sym(100)!( 99,100);
poly := sub<Sym(100)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
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