Polytope of Type {4,12,10,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,10,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,205032)
Rank : 5
Schlafli Type : {4,12,10,2}
Number of vertices, edges, etc : 4, 24, 60, 10, 2
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 : {2,12,10,2}*960, {4,6,10,2}*960a
3-fold quotients : {4,4,10,2}*640
4-fold quotients : {2,6,10,2}*480
5-fold quotients : {4,12,2,2}*384a
6-fold quotients : {2,4,10,2}*320, {4,2,10,2}*320
10-fold quotients : {2,12,2,2}*192, {4,6,2,2}*192a
12-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
15-fold quotients : {4,4,2,2}*128
20-fold quotients : {2,6,2,2}*96
24-fold quotients : {2,2,5,2}*80
30-fold quotients : {2,4,2,2}*64, {4,2,2,2}*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 := ( 61, 76)( 62, 77)( 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)( 91,106)
( 92,107)( 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);;
s1 := ( 1, 61)( 2, 62)( 3, 63)( 4, 64)( 5, 65)( 6, 71)( 7, 72)( 8, 73)
( 9, 74)( 10, 75)( 11, 66)( 12, 67)( 13, 68)( 14, 69)( 15, 70)( 16, 76)
( 17, 77)( 18, 78)( 19, 79)( 20, 80)( 21, 86)( 22, 87)( 23, 88)( 24, 89)
( 25, 90)( 26, 81)( 27, 82)( 28, 83)( 29, 84)( 30, 85)( 31, 91)( 32, 92)
( 33, 93)( 34, 94)( 35, 95)( 36,101)( 37,102)( 38,103)( 39,104)( 40,105)
( 41, 96)( 42, 97)( 43, 98)( 44, 99)( 45,100)( 46,106)( 47,107)( 48,108)
( 49,109)( 50,110)( 51,116)( 52,117)( 53,118)( 54,119)( 55,120)( 56,111)
( 57,112)( 58,113)( 59,114)( 60,115);;
s2 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 12, 15)( 13, 14)( 16, 21)
( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 36)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 42, 45)( 43, 44)( 46, 51)( 47, 55)( 48, 54)
( 49, 53)( 50, 52)( 57, 60)( 58, 59)( 61, 96)( 62,100)( 63, 99)( 64, 98)
( 65, 97)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71,101)( 72,105)
( 73,104)( 74,103)( 75,102)( 76,111)( 77,115)( 78,114)( 79,113)( 80,112)
( 81,106)( 82,110)( 83,109)( 84,108)( 85,107)( 86,116)( 87,120)( 88,119)
( 89,118)( 90,117);;
s3 := ( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)
( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)
( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)
( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)
( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)
(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)(118,120);;
s4 := (121,122);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(122)!( 61, 76)( 62, 77)( 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)
( 91,106)( 92,107)( 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);
s1 := Sym(122)!( 1, 61)( 2, 62)( 3, 63)( 4, 64)( 5, 65)( 6, 71)( 7, 72)
( 8, 73)( 9, 74)( 10, 75)( 11, 66)( 12, 67)( 13, 68)( 14, 69)( 15, 70)
( 16, 76)( 17, 77)( 18, 78)( 19, 79)( 20, 80)( 21, 86)( 22, 87)( 23, 88)
( 24, 89)( 25, 90)( 26, 81)( 27, 82)( 28, 83)( 29, 84)( 30, 85)( 31, 91)
( 32, 92)( 33, 93)( 34, 94)( 35, 95)( 36,101)( 37,102)( 38,103)( 39,104)
( 40,105)( 41, 96)( 42, 97)( 43, 98)( 44, 99)( 45,100)( 46,106)( 47,107)
( 48,108)( 49,109)( 50,110)( 51,116)( 52,117)( 53,118)( 54,119)( 55,120)
( 56,111)( 57,112)( 58,113)( 59,114)( 60,115);
s2 := Sym(122)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 12, 15)( 13, 14)
( 16, 21)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 36)
( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 42, 45)( 43, 44)( 46, 51)( 47, 55)
( 48, 54)( 49, 53)( 50, 52)( 57, 60)( 58, 59)( 61, 96)( 62,100)( 63, 99)
( 64, 98)( 65, 97)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71,101)
( 72,105)( 73,104)( 74,103)( 75,102)( 76,111)( 77,115)( 78,114)( 79,113)
( 80,112)( 81,106)( 82,110)( 83,109)( 84,108)( 85,107)( 86,116)( 87,120)
( 88,119)( 89,118)( 90,117);
s3 := Sym(122)!( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)
( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)
( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)
( 58, 60)( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)
( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)
( 98,100)(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)
(118,120);
s4 := Sym(122)!(121,122);
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*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope