Polytope of Type {12,4,10,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,10,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,205032)
Rank : 5
Schlafli Type : {12,4,10,2}
Number of vertices, edges, etc : 12, 24, 20, 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 : {12,2,10,2}*960, {6,4,10,2}*960
3-fold quotients : {4,4,10,2}*640
4-fold quotients : {12,2,5,2}*480, {6,2,10,2}*480
5-fold quotients : {12,4,2,2}*384a
6-fold quotients : {2,4,10,2}*320, {4,2,10,2}*320
8-fold quotients : {3,2,10,2}*240, {6,2,5,2}*240
10-fold quotients : {12,2,2,2}*192, {6,4,2,2}*192a
12-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
15-fold quotients : {4,4,2,2}*128
16-fold quotients : {3,2,5,2}*120
20-fold quotients : {6,2,2,2}*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 : {3,2,2,2}*48
60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)
( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)
( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 91)( 62, 92)( 63, 93)( 64, 94)
( 65, 95)( 66,101)( 67,102)( 68,103)( 69,104)( 70,105)( 71, 96)( 72, 97)
( 73, 98)( 74, 99)( 75,100)( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)
( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,111)( 87,112)( 88,113)
( 89,114)( 90,115);;
s1 := ( 1, 66)( 2, 67)( 3, 68)( 4, 69)( 5, 70)( 6, 61)( 7, 62)( 8, 63)
( 9, 64)( 10, 65)( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)( 16, 81)
( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 76)( 22, 77)( 23, 78)( 24, 79)
( 25, 80)( 26, 86)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 96)( 32, 97)
( 33, 98)( 34, 99)( 35,100)( 36, 91)( 37, 92)( 38, 93)( 39, 94)( 40, 95)
( 41,101)( 42,102)( 43,103)( 44,104)( 45,105)( 46,111)( 47,112)( 48,113)
( 49,114)( 50,115)( 51,106)( 52,107)( 53,108)( 54,109)( 55,110)( 56,116)
( 57,117)( 58,118)( 59,119)( 60,120);;
s2 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 81)( 67, 85)( 68, 84)
( 69, 83)( 70, 82)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)( 91,106)
( 92,110)( 93,109)( 94,108)( 95,107)( 96,111)( 97,115)( 98,114)( 99,113)
(100,112)(101,116)(102,120)(103,119)(104,118)(105,117);;
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(122)!( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)
( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)
( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 91)( 62, 92)( 63, 93)
( 64, 94)( 65, 95)( 66,101)( 67,102)( 68,103)( 69,104)( 70,105)( 71, 96)
( 72, 97)( 73, 98)( 74, 99)( 75,100)( 76,106)( 77,107)( 78,108)( 79,109)
( 80,110)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,111)( 87,112)
( 88,113)( 89,114)( 90,115);
s1 := Sym(122)!( 1, 66)( 2, 67)( 3, 68)( 4, 69)( 5, 70)( 6, 61)( 7, 62)
( 8, 63)( 9, 64)( 10, 65)( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)
( 16, 81)( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 76)( 22, 77)( 23, 78)
( 24, 79)( 25, 80)( 26, 86)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 96)
( 32, 97)( 33, 98)( 34, 99)( 35,100)( 36, 91)( 37, 92)( 38, 93)( 39, 94)
( 40, 95)( 41,101)( 42,102)( 43,103)( 44,104)( 45,105)( 46,111)( 47,112)
( 48,113)( 49,114)( 50,115)( 51,106)( 52,107)( 53,108)( 54,109)( 55,110)
( 56,116)( 57,117)( 58,118)( 59,119)( 60,120);
s2 := Sym(122)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 81)( 67, 85)
( 68, 84)( 69, 83)( 70, 82)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)
( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,111)( 97,115)( 98,114)
( 99,113)(100,112)(101,116)(102,120)(103,119)(104,118)(105,117);
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, 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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope