Polytope of Type {2,4,4,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,15}*1920a
if this polytope has a name.
Group : SmallGroup(1920,239472)
Rank : 5
Schlafli Type : {2,4,4,15}
Number of vertices, edges, etc : 2, 8, 16, 60, 15
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 : {2,2,4,15}*480
5-fold quotients : {2,4,4,3}*384a
20-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)(28,29)
(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)(59,62)
(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82);;
s2 := ( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(19,27)(20,28)
(21,29)(22,30)(23,31)(24,32)(25,33)(26,34)(35,43)(36,44)(37,45)(38,46)(39,47)
(40,48)(41,49)(42,50)(51,59)(52,60)(53,61)(54,62)(55,63)(56,64)(57,65)(58,66)
(67,75)(68,76)(69,77)(70,78)(71,79)(72,80)(73,81)(74,82);;
s3 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,67)(20,68)(21,70)(22,69)
(23,75)(24,76)(25,78)(26,77)(27,71)(28,72)(29,74)(30,73)(31,79)(32,80)(33,82)
(34,81)(35,51)(36,52)(37,54)(38,53)(39,59)(40,60)(41,62)(42,61)(43,55)(44,56)
(45,58)(46,57)(47,63)(48,64)(49,66)(50,65);;
s4 := ( 3,19)( 4,21)( 5,20)( 6,22)( 7,31)( 8,33)( 9,32)(10,34)(11,27)(12,29)
(13,28)(14,30)(15,23)(16,25)(17,24)(18,26)(35,67)(36,69)(37,68)(38,70)(39,79)
(40,81)(41,80)(42,82)(43,75)(44,77)(45,76)(46,78)(47,71)(48,73)(49,72)(50,74)
(52,53)(55,63)(56,65)(57,64)(58,66)(60,61);;
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,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(82)!(1,2);
s1 := Sym(82)!( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)
(28,29)(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)
(59,62)(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82);
s2 := Sym(82)!( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(19,27)
(20,28)(21,29)(22,30)(23,31)(24,32)(25,33)(26,34)(35,43)(36,44)(37,45)(38,46)
(39,47)(40,48)(41,49)(42,50)(51,59)(52,60)(53,61)(54,62)(55,63)(56,64)(57,65)
(58,66)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80)(73,81)(74,82);
s3 := Sym(82)!( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,67)(20,68)(21,70)
(22,69)(23,75)(24,76)(25,78)(26,77)(27,71)(28,72)(29,74)(30,73)(31,79)(32,80)
(33,82)(34,81)(35,51)(36,52)(37,54)(38,53)(39,59)(40,60)(41,62)(42,61)(43,55)
(44,56)(45,58)(46,57)(47,63)(48,64)(49,66)(50,65);
s4 := Sym(82)!( 3,19)( 4,21)( 5,20)( 6,22)( 7,31)( 8,33)( 9,32)(10,34)(11,27)
(12,29)(13,28)(14,30)(15,23)(16,25)(17,24)(18,26)(35,67)(36,69)(37,68)(38,70)
(39,79)(40,81)(41,80)(42,82)(43,75)(44,77)(45,76)(46,78)(47,71)(48,73)(49,72)
(50,74)(52,53)(55,63)(56,65)(57,64)(58,66)(60,61);
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*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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope