Polytope of Type {4,15,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,15,4,2}*960
if this polytope has a name.
Group : SmallGroup(960,11381)
Rank : 5
Schlafli Type : {4,15,4,2}
Number of vertices, edges, etc : 4, 30, 30, 4, 2
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,15,4,2,2} of size 1920
Vertex Figure Of :
{2,4,15,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
5-fold quotients : {4,3,4,2}*192
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,15,4,2}*1920a, {4,15,4,2}*1920b, {4,30,4,2}*1920d, {4,30,4,2}*1920e, {4,30,4,2}*1920f, {4,30,4,2}*1920g
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)
(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80);;
s1 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,65)(18,67)(19,66)(20,68)
(21,73)(22,75)(23,74)(24,76)(25,69)(26,71)(27,70)(28,72)(29,77)(30,79)(31,78)
(32,80)(33,49)(34,51)(35,50)(36,52)(37,57)(38,59)(39,58)(40,60)(41,53)(42,55)
(43,54)(44,56)(45,61)(46,63)(47,62)(48,64);;
s2 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,29)( 6,30)( 7,32)( 8,31)( 9,25)(10,26)
(11,28)(12,27)(13,21)(14,22)(15,24)(16,23)(33,65)(34,66)(35,68)(36,67)(37,77)
(38,78)(39,80)(40,79)(41,73)(42,74)(43,76)(44,75)(45,69)(46,70)(47,72)(48,71)
(51,52)(53,61)(54,62)(55,64)(56,63)(59,60);;
s3 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)
(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)
(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)
(65,68)(66,67)(69,72)(70,71)(73,76)(74,75)(77,80)(78,79);;
s4 := (81,82);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*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(82)!( 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)(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80);
s1 := Sym(82)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,65)(18,67)(19,66)
(20,68)(21,73)(22,75)(23,74)(24,76)(25,69)(26,71)(27,70)(28,72)(29,77)(30,79)
(31,78)(32,80)(33,49)(34,51)(35,50)(36,52)(37,57)(38,59)(39,58)(40,60)(41,53)
(42,55)(43,54)(44,56)(45,61)(46,63)(47,62)(48,64);
s2 := Sym(82)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,29)( 6,30)( 7,32)( 8,31)( 9,25)
(10,26)(11,28)(12,27)(13,21)(14,22)(15,24)(16,23)(33,65)(34,66)(35,68)(36,67)
(37,77)(38,78)(39,80)(40,79)(41,73)(42,74)(43,76)(44,75)(45,69)(46,70)(47,72)
(48,71)(51,52)(53,61)(54,62)(55,64)(56,63)(59,60);
s3 := Sym(82)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)
(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)
(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)
(62,63)(65,68)(66,67)(69,72)(70,71)(73,76)(74,75)(77,80)(78,79);
s4 := Sym(82)!(81,82);
poly := sub<Sym(82)|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,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*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