Polytope of Type {20,6,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,2,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 5
Schlafli Type : {20,6,2,2}
Number of vertices, edges, etc : 40, 120, 12, 2, 2
Order of s0s1s2s3s4 : 30
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 : {20,6,2,2}*960b
4-fold quotients : {10,6,2,2}*480
5-fold quotients : {4,6,2,2}*384
10-fold quotients : {4,3,2,2}*192, {4,6,2,2}*192b, {4,6,2,2}*192c
12-fold quotients : {10,2,2,2}*160
20-fold quotients : {4,3,2,2}*96, {2,6,2,2}*96
24-fold quotients : {5,2,2,2}*80
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, 3)( 2, 4)( 5, 19)( 6, 20)( 7, 17)( 8, 18)( 9, 15)( 10, 16)
( 11, 13)( 12, 14)( 21, 23)( 22, 24)( 25, 39)( 26, 40)( 27, 37)( 28, 38)
( 29, 35)( 30, 36)( 31, 33)( 32, 34)( 41, 43)( 42, 44)( 45, 59)( 46, 60)
( 47, 57)( 48, 58)( 49, 55)( 50, 56)( 51, 53)( 52, 54)( 61, 63)( 62, 64)
( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 75)( 70, 76)( 71, 73)( 72, 74)
( 81, 83)( 82, 84)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89, 95)( 90, 96)
( 91, 93)( 92, 94)(101,103)(102,104)(105,119)(106,120)(107,117)(108,118)
(109,115)(110,116)(111,113)(112,114);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9, 17)( 10, 19)( 11, 18)( 12, 20)
( 14, 15)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 25, 41)( 26, 43)( 27, 42)
( 28, 44)( 29, 57)( 30, 59)( 31, 58)( 32, 60)( 33, 53)( 34, 55)( 35, 54)
( 36, 56)( 37, 49)( 38, 51)( 39, 50)( 40, 52)( 61, 65)( 62, 67)( 63, 66)
( 64, 68)( 69, 77)( 70, 79)( 71, 78)( 72, 80)( 74, 75)( 81,105)( 82,107)
( 83,106)( 84,108)( 85,101)( 86,103)( 87,102)( 88,104)( 89,117)( 90,119)
( 91,118)( 92,120)( 93,113)( 94,115)( 95,114)( 96,116)( 97,109)( 98,111)
( 99,110)(100,112);;
s2 := ( 1,101)( 2,104)( 3,103)( 4,102)( 5,105)( 6,108)( 7,107)( 8,106)
( 9,109)( 10,112)( 11,111)( 12,110)( 13,113)( 14,116)( 15,115)( 16,114)
( 17,117)( 18,120)( 19,119)( 20,118)( 21, 81)( 22, 84)( 23, 83)( 24, 82)
( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 89)( 30, 92)( 31, 91)( 32, 90)
( 33, 93)( 34, 96)( 35, 95)( 36, 94)( 37, 97)( 38,100)( 39, 99)( 40, 98)
( 41, 61)( 42, 64)( 43, 63)( 44, 62)( 45, 65)( 46, 68)( 47, 67)( 48, 66)
( 49, 69)( 50, 72)( 51, 71)( 52, 70)( 53, 73)( 54, 76)( 55, 75)( 56, 74)
( 57, 77)( 58, 80)( 59, 79)( 60, 78);;
s3 := (121,122);;
s4 := (123,124);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(124)!( 1, 3)( 2, 4)( 5, 19)( 6, 20)( 7, 17)( 8, 18)( 9, 15)
( 10, 16)( 11, 13)( 12, 14)( 21, 23)( 22, 24)( 25, 39)( 26, 40)( 27, 37)
( 28, 38)( 29, 35)( 30, 36)( 31, 33)( 32, 34)( 41, 43)( 42, 44)( 45, 59)
( 46, 60)( 47, 57)( 48, 58)( 49, 55)( 50, 56)( 51, 53)( 52, 54)( 61, 63)
( 62, 64)( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 75)( 70, 76)( 71, 73)
( 72, 74)( 81, 83)( 82, 84)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89, 95)
( 90, 96)( 91, 93)( 92, 94)(101,103)(102,104)(105,119)(106,120)(107,117)
(108,118)(109,115)(110,116)(111,113)(112,114);
s1 := Sym(124)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9, 17)( 10, 19)( 11, 18)
( 12, 20)( 14, 15)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 25, 41)( 26, 43)
( 27, 42)( 28, 44)( 29, 57)( 30, 59)( 31, 58)( 32, 60)( 33, 53)( 34, 55)
( 35, 54)( 36, 56)( 37, 49)( 38, 51)( 39, 50)( 40, 52)( 61, 65)( 62, 67)
( 63, 66)( 64, 68)( 69, 77)( 70, 79)( 71, 78)( 72, 80)( 74, 75)( 81,105)
( 82,107)( 83,106)( 84,108)( 85,101)( 86,103)( 87,102)( 88,104)( 89,117)
( 90,119)( 91,118)( 92,120)( 93,113)( 94,115)( 95,114)( 96,116)( 97,109)
( 98,111)( 99,110)(100,112);
s2 := Sym(124)!( 1,101)( 2,104)( 3,103)( 4,102)( 5,105)( 6,108)( 7,107)
( 8,106)( 9,109)( 10,112)( 11,111)( 12,110)( 13,113)( 14,116)( 15,115)
( 16,114)( 17,117)( 18,120)( 19,119)( 20,118)( 21, 81)( 22, 84)( 23, 83)
( 24, 82)( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 89)( 30, 92)( 31, 91)
( 32, 90)( 33, 93)( 34, 96)( 35, 95)( 36, 94)( 37, 97)( 38,100)( 39, 99)
( 40, 98)( 41, 61)( 42, 64)( 43, 63)( 44, 62)( 45, 65)( 46, 68)( 47, 67)
( 48, 66)( 49, 69)( 50, 72)( 51, 71)( 52, 70)( 53, 73)( 54, 76)( 55, 75)
( 56, 74)( 57, 77)( 58, 80)( 59, 79)( 60, 78);
s3 := Sym(124)!(121,122);
s4 := Sym(124)!(123,124);
poly := sub<Sym(124)|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*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1 >;
to this polytope