Polytope of Type {2,6,20,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,20,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,205034)
Rank : 5
Schlafli Type : {2,6,20,4}
Number of vertices, edges, etc : 2, 6, 60, 40, 4
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
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) :
2-fold quotients : {2,6,20,2}*960a, {2,6,10,4}*960
3-fold quotients : {2,2,20,4}*640
4-fold quotients : {2,6,10,2}*480
5-fold quotients : {2,6,4,4}*384
6-fold quotients : {2,2,20,2}*320, {2,2,10,4}*320
10-fold quotients : {2,6,2,4}*192, {2,6,4,2}*192a
12-fold quotients : {2,2,10,2}*160
15-fold quotients : {2,2,4,4}*128
20-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
24-fold quotients : {2,2,5,2}*80
30-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
40-fold quotients : {2,3,2,2}*48
60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 8, 13)( 9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)( 25, 30)
( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 53, 58)
( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 68, 73)( 69, 74)( 70, 75)( 71, 76)
( 72, 77)( 83, 88)( 84, 89)( 85, 90)( 86, 91)( 87, 92)( 98,103)( 99,104)
(100,105)(101,106)(102,107)(113,118)(114,119)(115,120)(116,121)(117,122);;
s2 := ( 3, 8)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 17)( 15, 16)( 18, 23)
( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 29, 32)( 30, 31)( 33, 38)( 34, 42)
( 35, 41)( 36, 40)( 37, 39)( 44, 47)( 45, 46)( 48, 53)( 49, 57)( 50, 56)
( 51, 55)( 52, 54)( 59, 62)( 60, 61)( 63, 98)( 64,102)( 65,101)( 66,100)
( 67, 99)( 68, 93)( 69, 97)( 70, 96)( 71, 95)( 72, 94)( 73,103)( 74,107)
( 75,106)( 76,105)( 77,104)( 78,113)( 79,117)( 80,116)( 81,115)( 82,114)
( 83,108)( 84,112)( 85,111)( 86,110)( 87,109)( 88,118)( 89,122)( 90,121)
( 91,120)( 92,119);;
s3 := ( 3, 64)( 4, 63)( 5, 67)( 6, 66)( 7, 65)( 8, 69)( 9, 68)( 10, 72)
( 11, 71)( 12, 70)( 13, 74)( 14, 73)( 15, 77)( 16, 76)( 17, 75)( 18, 79)
( 19, 78)( 20, 82)( 21, 81)( 22, 80)( 23, 84)( 24, 83)( 25, 87)( 26, 86)
( 27, 85)( 28, 89)( 29, 88)( 30, 92)( 31, 91)( 32, 90)( 33, 94)( 34, 93)
( 35, 97)( 36, 96)( 37, 95)( 38, 99)( 39, 98)( 40,102)( 41,101)( 42,100)
( 43,104)( 44,103)( 45,107)( 46,106)( 47,105)( 48,109)( 49,108)( 50,112)
( 51,111)( 52,110)( 53,114)( 54,113)( 55,117)( 56,116)( 57,115)( 58,119)
( 59,118)( 60,122)( 61,121)( 62,120);;
s4 := ( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)( 70, 85)
( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 76, 91)( 77, 92)( 93,108)
( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)
(102,117)(103,118)(104,119)(105,120)(106,121)(107,122);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(122)!(1,2);
s1 := Sym(122)!( 8, 13)( 9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)
( 25, 30)( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)
( 53, 58)( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 68, 73)( 69, 74)( 70, 75)
( 71, 76)( 72, 77)( 83, 88)( 84, 89)( 85, 90)( 86, 91)( 87, 92)( 98,103)
( 99,104)(100,105)(101,106)(102,107)(113,118)(114,119)(115,120)(116,121)
(117,122);
s2 := Sym(122)!( 3, 8)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 17)( 15, 16)
( 18, 23)( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 29, 32)( 30, 31)( 33, 38)
( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 44, 47)( 45, 46)( 48, 53)( 49, 57)
( 50, 56)( 51, 55)( 52, 54)( 59, 62)( 60, 61)( 63, 98)( 64,102)( 65,101)
( 66,100)( 67, 99)( 68, 93)( 69, 97)( 70, 96)( 71, 95)( 72, 94)( 73,103)
( 74,107)( 75,106)( 76,105)( 77,104)( 78,113)( 79,117)( 80,116)( 81,115)
( 82,114)( 83,108)( 84,112)( 85,111)( 86,110)( 87,109)( 88,118)( 89,122)
( 90,121)( 91,120)( 92,119);
s3 := Sym(122)!( 3, 64)( 4, 63)( 5, 67)( 6, 66)( 7, 65)( 8, 69)( 9, 68)
( 10, 72)( 11, 71)( 12, 70)( 13, 74)( 14, 73)( 15, 77)( 16, 76)( 17, 75)
( 18, 79)( 19, 78)( 20, 82)( 21, 81)( 22, 80)( 23, 84)( 24, 83)( 25, 87)
( 26, 86)( 27, 85)( 28, 89)( 29, 88)( 30, 92)( 31, 91)( 32, 90)( 33, 94)
( 34, 93)( 35, 97)( 36, 96)( 37, 95)( 38, 99)( 39, 98)( 40,102)( 41,101)
( 42,100)( 43,104)( 44,103)( 45,107)( 46,106)( 47,105)( 48,109)( 49,108)
( 50,112)( 51,111)( 52,110)( 53,114)( 54,113)( 55,117)( 56,116)( 57,115)
( 58,119)( 59,118)( 60,122)( 61,121)( 62,120);
s4 := Sym(122)!( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)
( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 76, 91)( 77, 92)
( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)
(101,116)(102,117)(103,118)(104,119)(105,120)(106,121)(107,122);
poly := sub<Sym(122)|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*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope