Polytope of Type {2,2,4,15,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,15,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240412)
Rank : 6
Schlafli Type : {2,2,4,15,4}
Number of vertices, edges, etc : 2, 2, 4, 30, 30, 4
Order of s0s1s2s3s4s5 : 30
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,2,4,3,4}*384
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,13)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(11,19)(12,20)(21,29)(22,30)
(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(37,45)(38,46)(39,47)(40,48)(41,49)
(42,50)(43,51)(44,52)(53,61)(54,62)(55,63)(56,64)(57,65)(58,66)(59,67)(60,68)
(69,77)(70,78)(71,79)(72,80)(73,81)(74,82)(75,83)(76,84);;
s3 := ( 6, 7)( 9,13)(10,15)(11,14)(12,16)(18,19)(21,69)(22,71)(23,70)(24,72)
(25,77)(26,79)(27,78)(28,80)(29,73)(30,75)(31,74)(32,76)(33,81)(34,83)(35,82)
(36,84)(37,53)(38,55)(39,54)(40,56)(41,61)(42,63)(43,62)(44,64)(45,57)(46,59)
(47,58)(48,60)(49,65)(50,67)(51,66)(52,68);;
s4 := ( 5,21)( 6,22)( 7,24)( 8,23)( 9,33)(10,34)(11,36)(12,35)(13,29)(14,30)
(15,32)(16,31)(17,25)(18,26)(19,28)(20,27)(37,69)(38,70)(39,72)(40,71)(41,81)
(42,82)(43,84)(44,83)(45,77)(46,78)(47,80)(48,79)(49,73)(50,74)(51,76)(52,75)
(55,56)(57,65)(58,66)(59,68)(60,67)(63,64);;
s5 := ( 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)(81,84)(82,83);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s2*s3*s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5,
s2*s3*s4*s3*s2*s3*s4*s2*s3, s5*s4*s3*s5*s4*s5*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*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(84)!(1,2);
s1 := Sym(84)!(3,4);
s2 := Sym(84)!( 5,13)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(11,19)(12,20)(21,29)
(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(37,45)(38,46)(39,47)(40,48)
(41,49)(42,50)(43,51)(44,52)(53,61)(54,62)(55,63)(56,64)(57,65)(58,66)(59,67)
(60,68)(69,77)(70,78)(71,79)(72,80)(73,81)(74,82)(75,83)(76,84);
s3 := Sym(84)!( 6, 7)( 9,13)(10,15)(11,14)(12,16)(18,19)(21,69)(22,71)(23,70)
(24,72)(25,77)(26,79)(27,78)(28,80)(29,73)(30,75)(31,74)(32,76)(33,81)(34,83)
(35,82)(36,84)(37,53)(38,55)(39,54)(40,56)(41,61)(42,63)(43,62)(44,64)(45,57)
(46,59)(47,58)(48,60)(49,65)(50,67)(51,66)(52,68);
s4 := Sym(84)!( 5,21)( 6,22)( 7,24)( 8,23)( 9,33)(10,34)(11,36)(12,35)(13,29)
(14,30)(15,32)(16,31)(17,25)(18,26)(19,28)(20,27)(37,69)(38,70)(39,72)(40,71)
(41,81)(42,82)(43,84)(44,83)(45,77)(46,78)(47,80)(48,79)(49,73)(50,74)(51,76)
(52,75)(55,56)(57,65)(58,66)(59,68)(60,67)(63,64);
s5 := Sym(84)!( 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)(81,84)(82,83);
poly := sub<Sym(84)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s2*s3,
s5*s4*s3*s5*s4*s5*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*s3*s4*s3*s4 >;
to this polytope