Polytope of Type {2,4,20,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,20,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,205034)
Rank : 5
Schlafli Type : {2,4,20,6}
Number of vertices, edges, etc : 2, 4, 40, 60, 6
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 : {2,2,20,6}*960a, {2,4,10,6}*960
3-fold quotients : {2,4,20,2}*640
4-fold quotients : {2,2,10,6}*480
5-fold quotients : {2,4,4,6}*384
6-fold quotients : {2,2,20,2}*320, {2,4,10,2}*320
10-fold quotients : {2,2,4,6}*192a, {2,4,2,6}*192
12-fold quotients : {2,2,10,2}*160
15-fold quotients : {2,4,4,2}*128
20-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
24-fold quotients : {2,2,5,2}*80
30-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
40-fold quotients : {2,2,2,3}*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 := ( 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);;
s2 := ( 3, 63)( 4, 67)( 5, 66)( 6, 65)( 7, 64)( 8, 68)( 9, 72)( 10, 71)
( 11, 70)( 12, 69)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)( 18, 78)
( 19, 82)( 20, 81)( 21, 80)( 22, 79)( 23, 83)( 24, 87)( 25, 86)( 26, 85)
( 27, 84)( 28, 88)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 93)( 34, 97)
( 35, 96)( 36, 95)( 37, 94)( 38, 98)( 39,102)( 40,101)( 41,100)( 42, 99)
( 43,103)( 44,107)( 45,106)( 46,105)( 47,104)( 48,108)( 49,112)( 50,111)
( 51,110)( 52,109)( 53,113)( 54,117)( 55,116)( 56,115)( 57,114)( 58,118)
( 59,122)( 60,121)( 61,120)( 62,119);;
s3 := ( 3, 4)( 5, 7)( 8, 14)( 9, 13)( 10, 17)( 11, 16)( 12, 15)( 18, 19)
( 20, 22)( 23, 29)( 24, 28)( 25, 32)( 26, 31)( 27, 30)( 33, 34)( 35, 37)
( 38, 44)( 39, 43)( 40, 47)( 41, 46)( 42, 45)( 48, 49)( 50, 52)( 53, 59)
( 54, 58)( 55, 62)( 56, 61)( 57, 60)( 63, 94)( 64, 93)( 65, 97)( 66, 96)
( 67, 95)( 68,104)( 69,103)( 70,107)( 71,106)( 72,105)( 73, 99)( 74, 98)
( 75,102)( 76,101)( 77,100)( 78,109)( 79,108)( 80,112)( 81,111)( 82,110)
( 83,119)( 84,118)( 85,122)( 86,121)( 87,120)( 88,114)( 89,113)( 90,117)
( 91,116)( 92,115);;
s4 := ( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)( 20, 25)
( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)( 48, 53)
( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 68)( 64, 69)( 65, 70)( 66, 71)
( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93, 98)( 94, 99)
( 95,100)( 96,101)( 97,102)(108,113)(109,114)(110,115)(111,116)(112,117);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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)!( 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);
s2 := Sym(122)!( 3, 63)( 4, 67)( 5, 66)( 6, 65)( 7, 64)( 8, 68)( 9, 72)
( 10, 71)( 11, 70)( 12, 69)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)
( 18, 78)( 19, 82)( 20, 81)( 21, 80)( 22, 79)( 23, 83)( 24, 87)( 25, 86)
( 26, 85)( 27, 84)( 28, 88)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 93)
( 34, 97)( 35, 96)( 36, 95)( 37, 94)( 38, 98)( 39,102)( 40,101)( 41,100)
( 42, 99)( 43,103)( 44,107)( 45,106)( 46,105)( 47,104)( 48,108)( 49,112)
( 50,111)( 51,110)( 52,109)( 53,113)( 54,117)( 55,116)( 56,115)( 57,114)
( 58,118)( 59,122)( 60,121)( 61,120)( 62,119);
s3 := Sym(122)!( 3, 4)( 5, 7)( 8, 14)( 9, 13)( 10, 17)( 11, 16)( 12, 15)
( 18, 19)( 20, 22)( 23, 29)( 24, 28)( 25, 32)( 26, 31)( 27, 30)( 33, 34)
( 35, 37)( 38, 44)( 39, 43)( 40, 47)( 41, 46)( 42, 45)( 48, 49)( 50, 52)
( 53, 59)( 54, 58)( 55, 62)( 56, 61)( 57, 60)( 63, 94)( 64, 93)( 65, 97)
( 66, 96)( 67, 95)( 68,104)( 69,103)( 70,107)( 71,106)( 72,105)( 73, 99)
( 74, 98)( 75,102)( 76,101)( 77,100)( 78,109)( 79,108)( 80,112)( 81,111)
( 82,110)( 83,119)( 84,118)( 85,122)( 86,121)( 87,120)( 88,114)( 89,113)
( 90,117)( 91,116)( 92,115);
s4 := Sym(122)!( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)
( 20, 25)( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)
( 48, 53)( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 68)( 64, 69)( 65, 70)
( 66, 71)( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93, 98)
( 94, 99)( 95,100)( 96,101)( 97,102)(108,113)(109,114)(110,115)(111,116)
(112,117);
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*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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