Polytope of Type {4,4,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,4,2}*256
if this polytope has a name.
Group : SmallGroup(256,27633)
Rank : 5
Schlafli Type : {4,4,4,2}
Number of vertices, edges, etc : 4, 8, 8, 4, 2
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,4,4,2,2} of size 512
{4,4,4,2,3} of size 768
{4,4,4,2,5} of size 1280
{4,4,4,2,7} of size 1792
Vertex Figure Of :
{2,4,4,4,2} of size 512
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,4,2}*128, {4,4,2,2}*128, {4,2,4,2}*128
4-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64, {4,2,2,2}*64
8-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,4,4}*512, {4,8,4,2}*512a, {4,8,4,2}*512b, {4,8,4,2}*512c, {4,8,4,2}*512d, {4,4,8,2}*512a, {8,4,4,2}*512a, {4,4,8,2}*512b, {8,4,4,2}*512b, {4,4,4,2}*512a, {4,4,4,2}*512b
3-fold covers : {4,4,4,6}*768, {4,4,12,2}*768, {12,4,4,2}*768, {4,12,4,2}*768a
5-fold covers : {4,4,4,10}*1280, {4,4,20,2}*1280, {20,4,4,2}*1280, {4,20,4,2}*1280
7-fold covers : {4,4,4,14}*1792, {4,4,28,2}*1792, {28,4,4,2}*1792, {4,28,4,2}*1792
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,25)(18,26)
(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(33,41)(34,42)(35,43)(36,44)(37,45)
(38,46)(39,47)(40,48)(49,57)(50,58)(51,59)(52,60)(53,61)(54,62)(55,63)
(56,64);;
s1 := ( 9,13)(10,14)(11,15)(12,16)(17,19)(18,20)(21,23)(22,24)(25,31)(26,32)
(27,29)(28,30)(33,37)(34,38)(35,39)(36,40)(49,55)(50,56)(51,53)(52,54)(57,59)
(58,60)(61,63)(62,64);;
s2 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)
(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)(37,53)
(38,54)(39,55)(40,56)(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)
(48,64);;
s3 := ( 1,41)( 2,42)( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,33)(10,34)
(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,58)(18,57)(19,60)(20,59)(21,62)
(22,61)(23,64)(24,63)(25,50)(26,49)(27,52)(28,51)(29,54)(30,53)(31,56)
(32,55);;
s4 := (65,66);;
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*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,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(66)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,25)
(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(33,41)(34,42)(35,43)(36,44)
(37,45)(38,46)(39,47)(40,48)(49,57)(50,58)(51,59)(52,60)(53,61)(54,62)(55,63)
(56,64);
s1 := Sym(66)!( 9,13)(10,14)(11,15)(12,16)(17,19)(18,20)(21,23)(22,24)(25,31)
(26,32)(27,29)(28,30)(33,37)(34,38)(35,39)(36,40)(49,55)(50,56)(51,53)(52,54)
(57,59)(58,60)(61,63)(62,64);
s2 := Sym(66)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)
(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)
(37,53)(38,54)(39,55)(40,56)(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)
(48,64);
s3 := Sym(66)!( 1,41)( 2,42)( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,33)
(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,58)(18,57)(19,60)(20,59)
(21,62)(22,61)(23,64)(24,63)(25,50)(26,49)(27,52)(28,51)(29,54)(30,53)(31,56)
(32,55);
s4 := Sym(66)!(65,66);
poly := sub<Sym(66)|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*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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope