Polytope of Type {10,4,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,3}*480
Also Known As : {{10,4|2},{4,3}}. if this polytope has another name.
Group : SmallGroup(480,1193)
Rank : 4
Schlafli Type : {10,4,3}
Number of vertices, edges, etc : 10, 40, 12, 6
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,4,3,2} of size 960
   {10,4,3,3} of size 1920
   {10,4,3,4} of size 1920
Vertex Figure Of :
   {2,10,4,3} of size 960
   {4,10,4,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {10,2,3}*120
   5-fold quotients : {2,4,3}*96
   8-fold quotients : {5,2,3}*60
   10-fold quotients : {2,4,3}*48
   20-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,4,3}*960, {10,8,3}*960, {10,4,6}*960
   3-fold covers : {10,4,9}*1440, {10,12,3}*1440, {30,4,3}*1440
   4-fold covers : {20,8,3}*1920, {20,4,3}*1920, {10,8,3}*1920, {40,4,3}*1920, {10,4,12}*1920b, {20,4,6}*1920b, {10,4,6}*1920, {10,4,12}*1920c, {10,8,6}*1920a, {10,8,6}*1920b
Permutation Representation (GAP) :

s0 := (  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)( 12, 16)
( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)
( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)( 52, 56)
( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)
( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)(112,116);;
s1 := (  1, 67)(  2, 68)(  3, 65)(  4, 66)(  5, 63)(  6, 64)(  7, 61)(  8, 62)
(  9, 79)( 10, 80)( 11, 77)( 12, 78)( 13, 75)( 14, 76)( 15, 73)( 16, 74)
( 17, 71)( 18, 72)( 19, 69)( 20, 70)( 21, 87)( 22, 88)( 23, 85)( 24, 86)
( 25, 83)( 26, 84)( 27, 81)( 28, 82)( 29, 99)( 30,100)( 31, 97)( 32, 98)
( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 91)( 38, 92)( 39, 89)( 40, 90)
( 41,107)( 42,108)( 43,105)( 44,106)( 45,103)( 46,104)( 47,101)( 48,102)
( 49,119)( 50,120)( 51,117)( 52,118)( 53,115)( 54,116)( 55,113)( 56,114)
( 57,111)( 58,112)( 59,109)( 60,110);;
s2 := (  2,  3)(  6,  7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)( 23, 42)
( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)( 31, 50)
( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)( 39, 58)
( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)( 90,111)
( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)( 98,119)
( 99,118)(100,120);;
s3 := (  1, 41)(  2, 44)(  3, 43)(  4, 42)(  5, 45)(  6, 48)(  7, 47)(  8, 46)
(  9, 49)( 10, 52)( 11, 51)( 12, 50)( 13, 53)( 14, 56)( 15, 55)( 16, 54)
( 17, 57)( 18, 60)( 19, 59)( 20, 58)( 22, 24)( 26, 28)( 30, 32)( 34, 36)
( 38, 40)( 61,101)( 62,104)( 63,103)( 64,102)( 65,105)( 66,108)( 67,107)
( 68,106)( 69,109)( 70,112)( 71,111)( 72,110)( 73,113)( 74,116)( 75,115)
( 76,114)( 77,117)( 78,120)( 79,119)( 80,118)( 82, 84)( 86, 88)( 90, 92)
( 94, 96)( 98,100);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
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(120)!(  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)
( 12, 16)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)
( 32, 36)( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)
( 52, 56)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)
( 72, 76)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)
(112,116);
s1 := Sym(120)!(  1, 67)(  2, 68)(  3, 65)(  4, 66)(  5, 63)(  6, 64)(  7, 61)
(  8, 62)(  9, 79)( 10, 80)( 11, 77)( 12, 78)( 13, 75)( 14, 76)( 15, 73)
( 16, 74)( 17, 71)( 18, 72)( 19, 69)( 20, 70)( 21, 87)( 22, 88)( 23, 85)
( 24, 86)( 25, 83)( 26, 84)( 27, 81)( 28, 82)( 29, 99)( 30,100)( 31, 97)
( 32, 98)( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 91)( 38, 92)( 39, 89)
( 40, 90)( 41,107)( 42,108)( 43,105)( 44,106)( 45,103)( 46,104)( 47,101)
( 48,102)( 49,119)( 50,120)( 51,117)( 52,118)( 53,115)( 54,116)( 55,113)
( 56,114)( 57,111)( 58,112)( 59,109)( 60,110);
s2 := Sym(120)!(  2,  3)(  6,  7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)
( 23, 42)( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)
( 31, 50)( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)
( 39, 58)( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)
( 82,103)( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)
( 90,111)( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)
( 98,119)( 99,118)(100,120);
s3 := Sym(120)!(  1, 41)(  2, 44)(  3, 43)(  4, 42)(  5, 45)(  6, 48)(  7, 47)
(  8, 46)(  9, 49)( 10, 52)( 11, 51)( 12, 50)( 13, 53)( 14, 56)( 15, 55)
( 16, 54)( 17, 57)( 18, 60)( 19, 59)( 20, 58)( 22, 24)( 26, 28)( 30, 32)
( 34, 36)( 38, 40)( 61,101)( 62,104)( 63,103)( 64,102)( 65,105)( 66,108)
( 67,107)( 68,106)( 69,109)( 70,112)( 71,111)( 72,110)( 73,113)( 74,116)
( 75,115)( 76,114)( 77,117)( 78,120)( 79,119)( 80,118)( 82, 84)( 86, 88)
( 90, 92)( 94, 96)( 98,100);
poly := sub<Sym(120)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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