Polytope of Type {4,4,15,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,15,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,239472)
Rank : 5
Schlafli Type : {4,4,15,2}
Number of vertices, edges, etc : 8, 16, 60, 15, 2
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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) :
4-fold quotients : {2,4,15,2}*480
5-fold quotients : {4,4,3,2}*384a
20-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 7)( 6, 8)( 9,12)(10,11)(13,14)(15,16)(21,23)(22,24)(25,28)(26,27)
(29,30)(31,32)(37,39)(38,40)(41,44)(42,43)(45,46)(47,48)(53,55)(54,56)(57,60)
(58,59)(61,62)(63,64)(69,71)(70,72)(73,76)(74,75)(77,78)(79,80);;
s1 := ( 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);;
s2 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,65)(18,66)(19,68)(20,67)
(21,73)(22,74)(23,76)(24,75)(25,69)(26,70)(27,72)(28,71)(29,77)(30,78)(31,80)
(32,79)(33,49)(34,50)(35,52)(36,51)(37,57)(38,58)(39,60)(40,59)(41,53)(42,54)
(43,56)(44,55)(45,61)(46,62)(47,64)(48,63);;
s3 := ( 1,17)( 2,19)( 3,18)( 4,20)( 5,29)( 6,31)( 7,30)( 8,32)( 9,25)(10,27)
(11,26)(12,28)(13,21)(14,23)(15,22)(16,24)(33,65)(34,67)(35,66)(36,68)(37,77)
(38,79)(39,78)(40,80)(41,73)(42,75)(43,74)(44,76)(45,69)(46,71)(47,70)(48,72)
(50,51)(53,61)(54,63)(55,62)(56,64)(58,59);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*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(82)!( 5, 7)( 6, 8)( 9,12)(10,11)(13,14)(15,16)(21,23)(22,24)(25,28)
(26,27)(29,30)(31,32)(37,39)(38,40)(41,44)(42,43)(45,46)(47,48)(53,55)(54,56)
(57,60)(58,59)(61,62)(63,64)(69,71)(70,72)(73,76)(74,75)(77,78)(79,80);
s1 := 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);
s2 := Sym(82)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,65)(18,66)(19,68)
(20,67)(21,73)(22,74)(23,76)(24,75)(25,69)(26,70)(27,72)(28,71)(29,77)(30,78)
(31,80)(32,79)(33,49)(34,50)(35,52)(36,51)(37,57)(38,58)(39,60)(40,59)(41,53)
(42,54)(43,56)(44,55)(45,61)(46,62)(47,64)(48,63);
s3 := Sym(82)!( 1,17)( 2,19)( 3,18)( 4,20)( 5,29)( 6,31)( 7,30)( 8,32)( 9,25)
(10,27)(11,26)(12,28)(13,21)(14,23)(15,22)(16,24)(33,65)(34,67)(35,66)(36,68)
(37,77)(38,79)(39,78)(40,80)(41,73)(42,75)(43,74)(44,76)(45,69)(46,71)(47,70)
(48,72)(50,51)(53,61)(54,63)(55,62)(56,64)(58,59);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*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