Polytope of Type {2,2,20,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,20,12}*1920
if this polytope has a name.
Group : SmallGroup(1920,205047)
Rank : 5
Schlafli Type : {2,2,20,12}
Number of vertices, edges, etc : 2, 2, 20, 120, 12
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 : {2,2,10,12}*960, {2,2,20,6}*960a
3-fold quotients : {2,2,20,4}*640
4-fold quotients : {2,2,10,6}*480
5-fold quotients : {2,2,4,12}*384a
6-fold quotients : {2,2,20,2}*320, {2,2,10,4}*320
10-fold quotients : {2,2,2,12}*192, {2,2,4,6}*192a
12-fold quotients : {2,2,10,2}*160
15-fold quotients : {2,2,4,4}*128
20-fold quotients : {2,2,2,6}*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 : {2,2,2,3}*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 := (3,4);;
s2 := ( 6, 9)( 7, 8)( 11, 14)( 12, 13)( 16, 19)( 17, 18)( 21, 24)( 22, 23)
( 26, 29)( 27, 28)( 31, 34)( 32, 33)( 36, 39)( 37, 38)( 41, 44)( 42, 43)
( 46, 49)( 47, 48)( 51, 54)( 52, 53)( 56, 59)( 57, 58)( 61, 64)( 62, 63)
( 65, 95)( 66, 99)( 67, 98)( 68, 97)( 69, 96)( 70,100)( 71,104)( 72,103)
( 73,102)( 74,101)( 75,105)( 76,109)( 77,108)( 78,107)( 79,106)( 80,110)
( 81,114)( 82,113)( 83,112)( 84,111)( 85,115)( 86,119)( 87,118)( 88,117)
( 89,116)( 90,120)( 91,124)( 92,123)( 93,122)( 94,121);;
s3 := ( 5, 66)( 6, 65)( 7, 69)( 8, 68)( 9, 67)( 10, 76)( 11, 75)( 12, 79)
( 13, 78)( 14, 77)( 15, 71)( 16, 70)( 17, 74)( 18, 73)( 19, 72)( 20, 81)
( 21, 80)( 22, 84)( 23, 83)( 24, 82)( 25, 91)( 26, 90)( 27, 94)( 28, 93)
( 29, 92)( 30, 86)( 31, 85)( 32, 89)( 33, 88)( 34, 87)( 35, 96)( 36, 95)
( 37, 99)( 38, 98)( 39, 97)( 40,106)( 41,105)( 42,109)( 43,108)( 44,107)
( 45,101)( 46,100)( 47,104)( 48,103)( 49,102)( 50,111)( 51,110)( 52,114)
( 53,113)( 54,112)( 55,121)( 56,120)( 57,124)( 58,123)( 59,122)( 60,116)
( 61,115)( 62,119)( 63,118)( 64,117);;
s4 := ( 5, 10)( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 20, 25)( 21, 26)( 22, 27)
( 23, 28)( 24, 29)( 35, 40)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 50, 55)
( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 65, 85)( 66, 86)( 67, 87)( 68, 88)
( 69, 89)( 70, 80)( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 90)( 76, 91)
( 77, 92)( 78, 93)( 79, 94)( 95,115)( 96,116)( 97,117)( 98,118)( 99,119)
(100,110)(101,111)(102,112)(103,113)(104,114)(105,120)(106,121)(107,122)
(108,123)(109,124);;
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*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, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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(124)!(1,2);
s1 := Sym(124)!(3,4);
s2 := Sym(124)!( 6, 9)( 7, 8)( 11, 14)( 12, 13)( 16, 19)( 17, 18)( 21, 24)
( 22, 23)( 26, 29)( 27, 28)( 31, 34)( 32, 33)( 36, 39)( 37, 38)( 41, 44)
( 42, 43)( 46, 49)( 47, 48)( 51, 54)( 52, 53)( 56, 59)( 57, 58)( 61, 64)
( 62, 63)( 65, 95)( 66, 99)( 67, 98)( 68, 97)( 69, 96)( 70,100)( 71,104)
( 72,103)( 73,102)( 74,101)( 75,105)( 76,109)( 77,108)( 78,107)( 79,106)
( 80,110)( 81,114)( 82,113)( 83,112)( 84,111)( 85,115)( 86,119)( 87,118)
( 88,117)( 89,116)( 90,120)( 91,124)( 92,123)( 93,122)( 94,121);
s3 := Sym(124)!( 5, 66)( 6, 65)( 7, 69)( 8, 68)( 9, 67)( 10, 76)( 11, 75)
( 12, 79)( 13, 78)( 14, 77)( 15, 71)( 16, 70)( 17, 74)( 18, 73)( 19, 72)
( 20, 81)( 21, 80)( 22, 84)( 23, 83)( 24, 82)( 25, 91)( 26, 90)( 27, 94)
( 28, 93)( 29, 92)( 30, 86)( 31, 85)( 32, 89)( 33, 88)( 34, 87)( 35, 96)
( 36, 95)( 37, 99)( 38, 98)( 39, 97)( 40,106)( 41,105)( 42,109)( 43,108)
( 44,107)( 45,101)( 46,100)( 47,104)( 48,103)( 49,102)( 50,111)( 51,110)
( 52,114)( 53,113)( 54,112)( 55,121)( 56,120)( 57,124)( 58,123)( 59,122)
( 60,116)( 61,115)( 62,119)( 63,118)( 64,117);
s4 := Sym(124)!( 5, 10)( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 20, 25)( 21, 26)
( 22, 27)( 23, 28)( 24, 29)( 35, 40)( 36, 41)( 37, 42)( 38, 43)( 39, 44)
( 50, 55)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 65, 85)( 66, 86)( 67, 87)
( 68, 88)( 69, 89)( 70, 80)( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 90)
( 76, 91)( 77, 92)( 78, 93)( 79, 94)( 95,115)( 96,116)( 97,117)( 98,118)
( 99,119)(100,110)(101,111)(102,112)(103,113)(104,114)(105,120)(106,121)
(107,122)(108,123)(109,124);
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*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,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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