Polytope of Type {2,6,4,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4,20}*1920
if this polytope has a name.
Group : SmallGroup(1920,205034)
Rank : 5
Schlafli Type : {2,6,4,20}
Number of vertices, edges, etc : 2, 6, 12, 40, 20
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 : {2,6,2,20}*960, {2,6,4,10}*960
3-fold quotients : {2,2,4,20}*640
4-fold quotients : {2,3,2,20}*480, {2,6,2,10}*480
5-fold quotients : {2,6,4,4}*384
6-fold quotients : {2,2,2,20}*320, {2,2,4,10}*320
8-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
10-fold quotients : {2,6,2,4}*192, {2,6,4,2}*192a
12-fold quotients : {2,2,2,10}*160
15-fold quotients : {2,2,4,4}*128
16-fold quotients : {2,3,2,5}*120
20-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
24-fold quotients : {2,2,2,5}*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, 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, 83)( 64, 84)( 65, 85)( 66, 86)
( 67, 87)( 68, 78)( 69, 79)( 70, 80)( 71, 81)( 72, 82)( 73, 88)( 74, 89)
( 75, 90)( 76, 91)( 77, 92)( 93,113)( 94,114)( 95,115)( 96,116)( 97,117)
( 98,108)( 99,109)(100,110)(101,111)(102,112)(103,118)(104,119)(105,120)
(106,121)(107,122);;
s3 := ( 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);;
s4 := ( 3, 4)( 5, 7)( 8, 9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)( 20, 22)
( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)( 40, 42)
( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)( 60, 62)
( 63, 94)( 64, 93)( 65, 97)( 66, 96)( 67, 95)( 68, 99)( 69, 98)( 70,102)
( 71,101)( 72,100)( 73,104)( 74,103)( 75,107)( 76,106)( 77,105)( 78,109)
( 79,108)( 80,112)( 81,111)( 82,110)( 83,114)( 84,113)( 85,117)( 86,116)
( 87,115)( 88,119)( 89,118)( 90,122)( 91,121)( 92,120);;
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*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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, 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, 83)( 64, 84)( 65, 85)
( 66, 86)( 67, 87)( 68, 78)( 69, 79)( 70, 80)( 71, 81)( 72, 82)( 73, 88)
( 74, 89)( 75, 90)( 76, 91)( 77, 92)( 93,113)( 94,114)( 95,115)( 96,116)
( 97,117)( 98,108)( 99,109)(100,110)(101,111)(102,112)(103,118)(104,119)
(105,120)(106,121)(107,122);
s3 := 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);
s4 := Sym(122)!( 3, 4)( 5, 7)( 8, 9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)
( 20, 22)( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)
( 40, 42)( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)
( 60, 62)( 63, 94)( 64, 93)( 65, 97)( 66, 96)( 67, 95)( 68, 99)( 69, 98)
( 70,102)( 71,101)( 72,100)( 73,104)( 74,103)( 75,107)( 76,106)( 77,105)
( 78,109)( 79,108)( 80,112)( 81,111)( 82,110)( 83,114)( 84,113)( 85,117)
( 86,116)( 87,115)( 88,119)( 89,118)( 90,122)( 91,121)( 92,120);
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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope