Polytope of Type {2,2,10,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,6,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 6
Schlafli Type : {2,2,10,6,4}
Number of vertices, edges, etc : 2, 2, 10, 30, 12, 4
Order of s0s1s2s3s4s5 : 30
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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) :
5-fold quotients : {2,2,2,6,4}*384c
10-fold quotients : {2,2,2,3,4}*192
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, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 21)( 14, 23)( 15, 22)( 16, 24)
( 18, 19)( 25, 49)( 26, 51)( 27, 50)( 28, 52)( 29, 45)( 30, 47)( 31, 46)
( 32, 48)( 33, 61)( 34, 63)( 35, 62)( 36, 64)( 37, 57)( 38, 59)( 39, 58)
( 40, 60)( 41, 53)( 42, 55)( 43, 54)( 44, 56)( 65, 69)( 66, 71)( 67, 70)
( 68, 72)( 73, 81)( 74, 83)( 75, 82)( 76, 84)( 78, 79)( 85,109)( 86,111)
( 87,110)( 88,112)( 89,105)( 90,107)( 91,106)( 92,108)( 93,121)( 94,123)
( 95,122)( 96,124)( 97,117)( 98,119)( 99,118)(100,120)(101,113)(102,115)
(103,114)(104,116);;
s4 := ( 5, 85)( 6, 86)( 7, 88)( 8, 87)( 9, 89)( 10, 90)( 11, 92)( 12, 91)
( 13, 93)( 14, 94)( 15, 96)( 16, 95)( 17, 97)( 18, 98)( 19,100)( 20, 99)
( 21,101)( 22,102)( 23,104)( 24,103)( 25, 65)( 26, 66)( 27, 68)( 28, 67)
( 29, 69)( 30, 70)( 31, 72)( 32, 71)( 33, 73)( 34, 74)( 35, 76)( 36, 75)
( 37, 77)( 38, 78)( 39, 80)( 40, 79)( 41, 81)( 42, 82)( 43, 84)( 44, 83)
( 45,105)( 46,106)( 47,108)( 48,107)( 49,109)( 50,110)( 51,112)( 52,111)
( 53,113)( 54,114)( 55,116)( 56,115)( 57,117)( 58,118)( 59,120)( 60,119)
( 61,121)( 62,122)( 63,124)( 64,123);;
s5 := ( 5, 8)( 6, 7)( 9, 12)( 10, 11)( 13, 16)( 14, 15)( 17, 20)( 18, 19)
( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)( 33, 36)( 34, 35)
( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49, 52)( 50, 51)
( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)( 65, 68)( 66, 67)
( 69, 72)( 70, 71)( 73, 76)( 74, 75)( 77, 80)( 78, 79)( 81, 84)( 82, 83)
( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)( 97,100)( 98, 99)
(101,104)(102,103)(105,108)(106,107)(109,112)(110,111)(113,116)(114,115)
(117,120)(118,119)(121,124)(122,123);;
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,
s2*s3*s4*s3*s2*s3*s4*s3, s4*s5*s4*s5*s4*s5*s4*s5,
s5*s4*s3*s5*s4*s5*s4*s3*s4, s3*s4*s3*s4*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, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 21)( 14, 23)( 15, 22)
( 16, 24)( 18, 19)( 25, 49)( 26, 51)( 27, 50)( 28, 52)( 29, 45)( 30, 47)
( 31, 46)( 32, 48)( 33, 61)( 34, 63)( 35, 62)( 36, 64)( 37, 57)( 38, 59)
( 39, 58)( 40, 60)( 41, 53)( 42, 55)( 43, 54)( 44, 56)( 65, 69)( 66, 71)
( 67, 70)( 68, 72)( 73, 81)( 74, 83)( 75, 82)( 76, 84)( 78, 79)( 85,109)
( 86,111)( 87,110)( 88,112)( 89,105)( 90,107)( 91,106)( 92,108)( 93,121)
( 94,123)( 95,122)( 96,124)( 97,117)( 98,119)( 99,118)(100,120)(101,113)
(102,115)(103,114)(104,116);
s4 := Sym(124)!( 5, 85)( 6, 86)( 7, 88)( 8, 87)( 9, 89)( 10, 90)( 11, 92)
( 12, 91)( 13, 93)( 14, 94)( 15, 96)( 16, 95)( 17, 97)( 18, 98)( 19,100)
( 20, 99)( 21,101)( 22,102)( 23,104)( 24,103)( 25, 65)( 26, 66)( 27, 68)
( 28, 67)( 29, 69)( 30, 70)( 31, 72)( 32, 71)( 33, 73)( 34, 74)( 35, 76)
( 36, 75)( 37, 77)( 38, 78)( 39, 80)( 40, 79)( 41, 81)( 42, 82)( 43, 84)
( 44, 83)( 45,105)( 46,106)( 47,108)( 48,107)( 49,109)( 50,110)( 51,112)
( 52,111)( 53,113)( 54,114)( 55,116)( 56,115)( 57,117)( 58,118)( 59,120)
( 60,119)( 61,121)( 62,122)( 63,124)( 64,123);
s5 := Sym(124)!( 5, 8)( 6, 7)( 9, 12)( 10, 11)( 13, 16)( 14, 15)( 17, 20)
( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)( 33, 36)
( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49, 52)
( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)( 65, 68)
( 66, 67)( 69, 72)( 70, 71)( 73, 76)( 74, 75)( 77, 80)( 78, 79)( 81, 84)
( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)( 97,100)
( 98, 99)(101,104)(102,103)(105,108)(106,107)(109,112)(110,111)(113,116)
(114,115)(117,120)(118,119)(121,124)(122,123);
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, s2*s3*s4*s3*s2*s3*s4*s3,
s4*s5*s4*s5*s4*s5*s4*s5, s5*s4*s3*s5*s4*s5*s4*s3*s4,
s3*s4*s3*s4*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