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Polytope of Type {2,10,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,4,12}*1920
if this polytope has a name.
Group : SmallGroup(1920,205032)
Rank : 5
Schlafli Type : {2,10,4,12}
Number of vertices, edges, etc : 2, 10, 20, 24, 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 : {2,10,2,12}*960, {2,10,4,6}*960
   3-fold quotients : {2,10,4,4}*640
   4-fold quotients : {2,5,2,12}*480, {2,10,2,6}*480
   5-fold quotients : {2,2,4,12}*384a
   6-fold quotients : {2,10,2,4}*320, {2,10,4,2}*320
   8-fold quotients : {2,5,2,6}*240, {2,10,2,3}*240
   10-fold quotients : {2,2,2,12}*192, {2,2,4,6}*192a
   12-fold quotients : {2,5,2,4}*160, {2,10,2,2}*160
   15-fold quotients : {2,2,4,4}*128
   16-fold quotients : {2,5,2,3}*120
   20-fold quotients : {2,2,2,6}*96
   24-fold quotients : {2,5,2,2}*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 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)( 60, 61)
( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)( 80, 81)
( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101)
(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)(120,121);;
s2 := (  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, 79)( 64, 78)( 65, 82)( 66, 81)( 67, 80)( 68, 84)( 69, 83)( 70, 87)
( 71, 86)( 72, 85)( 73, 89)( 74, 88)( 75, 92)( 76, 91)( 77, 90)( 93,109)
( 94,108)( 95,112)( 96,111)( 97,110)( 98,114)( 99,113)(100,117)(101,116)
(102,115)(103,119)(104,118)(105,122)(106,121)(107,120);;
s3 := (  3, 63)(  4, 64)(  5, 65)(  6, 66)(  7, 67)(  8, 73)(  9, 74)( 10, 75)
( 11, 76)( 12, 77)( 13, 68)( 14, 69)( 15, 70)( 16, 71)( 17, 72)( 18, 78)
( 19, 79)( 20, 80)( 21, 81)( 22, 82)( 23, 88)( 24, 89)( 25, 90)( 26, 91)
( 27, 92)( 28, 83)( 29, 84)( 30, 85)( 31, 86)( 32, 87)( 33, 93)( 34, 94)
( 35, 95)( 36, 96)( 37, 97)( 38,103)( 39,104)( 40,105)( 41,106)( 42,107)
( 43, 98)( 44, 99)( 45,100)( 46,101)( 47,102)( 48,108)( 49,109)( 50,110)
( 51,111)( 52,112)( 53,118)( 54,119)( 55,120)( 56,121)( 57,122)( 58,113)
( 59,114)( 60,115)( 61,116)( 62,117);;
s4 := (  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, 98)( 64, 99)( 65,100)( 66,101)
( 67,102)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)( 73,103)( 74,104)
( 75,105)( 76,106)( 77,107)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)
( 83,108)( 84,109)( 85,110)( 86,111)( 87,112)( 88,118)( 89,119)( 90,120)
( 91,121)( 92,122);;
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*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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(122)!(1,2);
s1 := Sym(122)!(  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)
( 60, 61)( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)
( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)
(100,101)(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)
(120,121);
s2 := 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, 79)( 64, 78)( 65, 82)( 66, 81)( 67, 80)( 68, 84)( 69, 83)
( 70, 87)( 71, 86)( 72, 85)( 73, 89)( 74, 88)( 75, 92)( 76, 91)( 77, 90)
( 93,109)( 94,108)( 95,112)( 96,111)( 97,110)( 98,114)( 99,113)(100,117)
(101,116)(102,115)(103,119)(104,118)(105,122)(106,121)(107,120);
s3 := Sym(122)!(  3, 63)(  4, 64)(  5, 65)(  6, 66)(  7, 67)(  8, 73)(  9, 74)
( 10, 75)( 11, 76)( 12, 77)( 13, 68)( 14, 69)( 15, 70)( 16, 71)( 17, 72)
( 18, 78)( 19, 79)( 20, 80)( 21, 81)( 22, 82)( 23, 88)( 24, 89)( 25, 90)
( 26, 91)( 27, 92)( 28, 83)( 29, 84)( 30, 85)( 31, 86)( 32, 87)( 33, 93)
( 34, 94)( 35, 95)( 36, 96)( 37, 97)( 38,103)( 39,104)( 40,105)( 41,106)
( 42,107)( 43, 98)( 44, 99)( 45,100)( 46,101)( 47,102)( 48,108)( 49,109)
( 50,110)( 51,111)( 52,112)( 53,118)( 54,119)( 55,120)( 56,121)( 57,122)
( 58,113)( 59,114)( 60,115)( 61,116)( 62,117);
s4 := 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, 98)( 64, 99)( 65,100)
( 66,101)( 67,102)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)( 73,103)
( 74,104)( 75,105)( 76,106)( 77,107)( 78,113)( 79,114)( 80,115)( 81,116)
( 82,117)( 83,108)( 84,109)( 85,110)( 86,111)( 87,112)( 88,118)( 89,119)
( 90,120)( 91,121)( 92,122);
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*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*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 >; 
 

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