Polytope of Type {2,20,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,6,4}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240408)
Rank : 5
Schlafli Type : {2,20,6,4}
Number of vertices, edges, etc : 2, 20, 60, 12, 4
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) :
5-fold quotients : {2,4,6,4}*384f
10-fold quotients : {2,4,3,4}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(19,75)(20,76)
(21,77)(22,78)(23,79)(24,80)(25,81)(26,82)(27,67)(28,68)(29,69)(30,70)(31,71)
(32,72)(33,73)(34,74)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,65)(42,66)
(43,51)(44,52)(45,53)(46,54)(47,55)(48,56)(49,57)(50,58);;
s2 := ( 3,19)( 4,21)( 5,20)( 6,22)( 7,27)( 8,29)( 9,28)(10,30)(11,23)(12,25)
(13,24)(14,26)(15,31)(16,33)(17,32)(18,34)(35,67)(36,69)(37,68)(38,70)(39,75)
(40,77)(41,76)(42,78)(43,71)(44,73)(45,72)(46,74)(47,79)(48,81)(49,80)(50,82)
(52,53)(55,59)(56,61)(57,60)(58,62)(64,65);;
s3 := ( 5, 6)( 7,15)( 8,16)( 9,18)(10,17)(13,14)(21,22)(23,31)(24,32)(25,34)
(26,33)(29,30)(37,38)(39,47)(40,48)(41,50)(42,49)(45,46)(53,54)(55,63)(56,64)
(57,66)(58,65)(61,62)(69,70)(71,79)(72,80)(73,82)(74,81)(77,78);;
s4 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)
(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37)(39,42)(40,41)(43,46)
(44,45)(47,50)(48,49)(51,54)(52,53)(55,58)(56,57)(59,62)(60,61)(63,66)(64,65)
(67,70)(68,69)(71,74)(72,73)(75,78)(76,77)(79,82)(80,81);;
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*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(82)!(1,2);
s1 := Sym(82)!( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(19,75)
(20,76)(21,77)(22,78)(23,79)(24,80)(25,81)(26,82)(27,67)(28,68)(29,69)(30,70)
(31,71)(32,72)(33,73)(34,74)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,65)
(42,66)(43,51)(44,52)(45,53)(46,54)(47,55)(48,56)(49,57)(50,58);
s2 := Sym(82)!( 3,19)( 4,21)( 5,20)( 6,22)( 7,27)( 8,29)( 9,28)(10,30)(11,23)
(12,25)(13,24)(14,26)(15,31)(16,33)(17,32)(18,34)(35,67)(36,69)(37,68)(38,70)
(39,75)(40,77)(41,76)(42,78)(43,71)(44,73)(45,72)(46,74)(47,79)(48,81)(49,80)
(50,82)(52,53)(55,59)(56,61)(57,60)(58,62)(64,65);
s3 := Sym(82)!( 5, 6)( 7,15)( 8,16)( 9,18)(10,17)(13,14)(21,22)(23,31)(24,32)
(25,34)(26,33)(29,30)(37,38)(39,47)(40,48)(41,50)(42,49)(45,46)(53,54)(55,63)
(56,64)(57,66)(58,65)(61,62)(69,70)(71,79)(72,80)(73,82)(74,81)(77,78);
s4 := Sym(82)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)
(20,21)(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37)(39,42)(40,41)
(43,46)(44,45)(47,50)(48,49)(51,54)(52,53)(55,58)(56,57)(59,62)(60,61)(63,66)
(64,65)(67,70)(68,69)(71,74)(72,73)(75,78)(76,77)(79,82)(80,81);
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, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1 >;
to this polytope