Polytope of Type {2,2,10,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,4,3}*1920
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 6
Schlafli Type : {2,2,10,4,3}
Number of vertices, edges, etc : 2, 2, 10, 40, 12, 6
Order of s0s1s2s3s4s5 : 30
Order of s0s1s2s3s4s5s4s3s2s1 : 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) :
4-fold quotients : {2,2,10,2,3}*480
5-fold quotients : {2,2,2,4,3}*384
8-fold quotients : {2,2,5,2,3}*240
10-fold quotients : {2,2,2,4,3}*192
20-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 9, 21)( 10, 22)( 11, 23)( 12, 24)( 13, 17)( 14, 18)( 15, 19)( 16, 20)
( 29, 41)( 30, 42)( 31, 43)( 32, 44)( 33, 37)( 34, 38)( 35, 39)( 36, 40)
( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)( 56, 60)
( 69, 81)( 70, 82)( 71, 83)( 72, 84)( 73, 77)( 74, 78)( 75, 79)( 76, 80)
( 89,101)( 90,102)( 91,103)( 92,104)( 93, 97)( 94, 98)( 95, 99)( 96,100)
(109,121)(110,122)(111,123)(112,124)(113,117)(114,118)(115,119)(116,120);;
s3 := ( 5, 71)( 6, 72)( 7, 69)( 8, 70)( 9, 67)( 10, 68)( 11, 65)( 12, 66)
( 13, 83)( 14, 84)( 15, 81)( 16, 82)( 17, 79)( 18, 80)( 19, 77)( 20, 78)
( 21, 75)( 22, 76)( 23, 73)( 24, 74)( 25, 91)( 26, 92)( 27, 89)( 28, 90)
( 29, 87)( 30, 88)( 31, 85)( 32, 86)( 33,103)( 34,104)( 35,101)( 36,102)
( 37, 99)( 38,100)( 39, 97)( 40, 98)( 41, 95)( 42, 96)( 43, 93)( 44, 94)
( 45,111)( 46,112)( 47,109)( 48,110)( 49,107)( 50,108)( 51,105)( 52,106)
( 53,123)( 54,124)( 55,121)( 56,122)( 57,119)( 58,120)( 59,117)( 60,118)
( 61,115)( 62,116)( 63,113)( 64,114);;
s4 := ( 6, 7)( 10, 11)( 14, 15)( 18, 19)( 22, 23)( 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)( 41, 61)( 42, 63)( 43, 62)
( 44, 64)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 82, 83)( 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)(101,121)(102,123)
(103,122)(104,124);;
s5 := ( 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)
( 21, 61)( 22, 64)( 23, 63)( 24, 62)( 26, 28)( 30, 32)( 34, 36)( 38, 40)
( 42, 44)( 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)( 81,121)( 82,124)( 83,123)( 84,122)( 86, 88)( 90, 92)( 94, 96)
( 98,100)(102,104);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3,
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(124)!(1,2);
s1 := Sym(124)!(3,4);
s2 := Sym(124)!( 9, 21)( 10, 22)( 11, 23)( 12, 24)( 13, 17)( 14, 18)( 15, 19)
( 16, 20)( 29, 41)( 30, 42)( 31, 43)( 32, 44)( 33, 37)( 34, 38)( 35, 39)
( 36, 40)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)
( 56, 60)( 69, 81)( 70, 82)( 71, 83)( 72, 84)( 73, 77)( 74, 78)( 75, 79)
( 76, 80)( 89,101)( 90,102)( 91,103)( 92,104)( 93, 97)( 94, 98)( 95, 99)
( 96,100)(109,121)(110,122)(111,123)(112,124)(113,117)(114,118)(115,119)
(116,120);
s3 := Sym(124)!( 5, 71)( 6, 72)( 7, 69)( 8, 70)( 9, 67)( 10, 68)( 11, 65)
( 12, 66)( 13, 83)( 14, 84)( 15, 81)( 16, 82)( 17, 79)( 18, 80)( 19, 77)
( 20, 78)( 21, 75)( 22, 76)( 23, 73)( 24, 74)( 25, 91)( 26, 92)( 27, 89)
( 28, 90)( 29, 87)( 30, 88)( 31, 85)( 32, 86)( 33,103)( 34,104)( 35,101)
( 36,102)( 37, 99)( 38,100)( 39, 97)( 40, 98)( 41, 95)( 42, 96)( 43, 93)
( 44, 94)( 45,111)( 46,112)( 47,109)( 48,110)( 49,107)( 50,108)( 51,105)
( 52,106)( 53,123)( 54,124)( 55,121)( 56,122)( 57,119)( 58,120)( 59,117)
( 60,118)( 61,115)( 62,116)( 63,113)( 64,114);
s4 := Sym(124)!( 6, 7)( 10, 11)( 14, 15)( 18, 19)( 22, 23)( 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)( 41, 61)( 42, 63)
( 43, 62)( 44, 64)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 82, 83)( 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)(101,121)
(102,123)(103,122)(104,124);
s5 := Sym(124)!( 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)( 21, 61)( 22, 64)( 23, 63)( 24, 62)( 26, 28)( 30, 32)( 34, 36)
( 38, 40)( 42, 44)( 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)( 81,121)( 82,124)( 83,123)( 84,122)( 86, 88)( 90, 92)
( 94, 96)( 98,100)(102,104);
poly := sub<Sym(124)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3,
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 >;
to this polytope