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Polytope of Type {2,18,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,14}*1008
if this polytope has a name.
Group : SmallGroup(1008,507)
Rank : 4
Schlafli Type : {2,18,14}
Number of vertices, edges, etc : 2, 18, 126, 14
Order of s0s1s2s3 : 126
Order of s0s1s2s3s2s1 : 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) :
   3-fold quotients : {2,6,14}*336
   7-fold quotients : {2,18,2}*144
   9-fold quotients : {2,2,14}*112
   14-fold quotients : {2,9,2}*72
   18-fold quotients : {2,2,7}*56
   21-fold quotients : {2,6,2}*48
   42-fold quotients : {2,3,2}*24
   63-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 24, 46)
( 25, 45)( 26, 47)( 27, 49)( 28, 48)( 29, 50)( 30, 52)( 31, 51)( 32, 53)
( 33, 55)( 34, 54)( 35, 56)( 36, 58)( 37, 57)( 38, 59)( 39, 61)( 40, 60)
( 41, 62)( 42, 64)( 43, 63)( 44, 65)( 67, 68)( 70, 71)( 73, 74)( 76, 77)
( 79, 80)( 82, 83)( 85, 86)( 87,109)( 88,108)( 89,110)( 90,112)( 91,111)
( 92,113)( 93,115)( 94,114)( 95,116)( 96,118)( 97,117)( 98,119)( 99,121)
(100,120)(101,122)(102,124)(103,123)(104,125)(105,127)(106,126)(107,128);;
s2 := (  3, 24)(  4, 26)(  5, 25)(  6, 42)(  7, 44)(  8, 43)(  9, 39)( 10, 41)
( 11, 40)( 12, 36)( 13, 38)( 14, 37)( 15, 33)( 16, 35)( 17, 34)( 18, 30)
( 19, 32)( 20, 31)( 21, 27)( 22, 29)( 23, 28)( 45, 46)( 48, 64)( 49, 63)
( 50, 65)( 51, 61)( 52, 60)( 53, 62)( 54, 58)( 55, 57)( 56, 59)( 66, 87)
( 67, 89)( 68, 88)( 69,105)( 70,107)( 71,106)( 72,102)( 73,104)( 74,103)
( 75, 99)( 76,101)( 77,100)( 78, 96)( 79, 98)( 80, 97)( 81, 93)( 82, 95)
( 83, 94)( 84, 90)( 85, 92)( 86, 91)(108,109)(111,127)(112,126)(113,128)
(114,124)(115,123)(116,125)(117,121)(118,120)(119,122);;
s3 := (  3, 69)(  4, 70)(  5, 71)(  6, 66)(  7, 67)(  8, 68)(  9, 84)( 10, 85)
( 11, 86)( 12, 81)( 13, 82)( 14, 83)( 15, 78)( 16, 79)( 17, 80)( 18, 75)
( 19, 76)( 20, 77)( 21, 72)( 22, 73)( 23, 74)( 24, 90)( 25, 91)( 26, 92)
( 27, 87)( 28, 88)( 29, 89)( 30,105)( 31,106)( 32,107)( 33,102)( 34,103)
( 35,104)( 36, 99)( 37,100)( 38,101)( 39, 96)( 40, 97)( 41, 98)( 42, 93)
( 43, 94)( 44, 95)( 45,111)( 46,112)( 47,113)( 48,108)( 49,109)( 50,110)
( 51,126)( 52,127)( 53,128)( 54,123)( 55,124)( 56,125)( 57,120)( 58,121)
( 59,122)( 60,117)( 61,118)( 62,119)( 63,114)( 64,115)( 65,116);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
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*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(128)!(1,2);
s1 := Sym(128)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 24, 46)( 25, 45)( 26, 47)( 27, 49)( 28, 48)( 29, 50)( 30, 52)( 31, 51)
( 32, 53)( 33, 55)( 34, 54)( 35, 56)( 36, 58)( 37, 57)( 38, 59)( 39, 61)
( 40, 60)( 41, 62)( 42, 64)( 43, 63)( 44, 65)( 67, 68)( 70, 71)( 73, 74)
( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 87,109)( 88,108)( 89,110)( 90,112)
( 91,111)( 92,113)( 93,115)( 94,114)( 95,116)( 96,118)( 97,117)( 98,119)
( 99,121)(100,120)(101,122)(102,124)(103,123)(104,125)(105,127)(106,126)
(107,128);
s2 := Sym(128)!(  3, 24)(  4, 26)(  5, 25)(  6, 42)(  7, 44)(  8, 43)(  9, 39)
( 10, 41)( 11, 40)( 12, 36)( 13, 38)( 14, 37)( 15, 33)( 16, 35)( 17, 34)
( 18, 30)( 19, 32)( 20, 31)( 21, 27)( 22, 29)( 23, 28)( 45, 46)( 48, 64)
( 49, 63)( 50, 65)( 51, 61)( 52, 60)( 53, 62)( 54, 58)( 55, 57)( 56, 59)
( 66, 87)( 67, 89)( 68, 88)( 69,105)( 70,107)( 71,106)( 72,102)( 73,104)
( 74,103)( 75, 99)( 76,101)( 77,100)( 78, 96)( 79, 98)( 80, 97)( 81, 93)
( 82, 95)( 83, 94)( 84, 90)( 85, 92)( 86, 91)(108,109)(111,127)(112,126)
(113,128)(114,124)(115,123)(116,125)(117,121)(118,120)(119,122);
s3 := Sym(128)!(  3, 69)(  4, 70)(  5, 71)(  6, 66)(  7, 67)(  8, 68)(  9, 84)
( 10, 85)( 11, 86)( 12, 81)( 13, 82)( 14, 83)( 15, 78)( 16, 79)( 17, 80)
( 18, 75)( 19, 76)( 20, 77)( 21, 72)( 22, 73)( 23, 74)( 24, 90)( 25, 91)
( 26, 92)( 27, 87)( 28, 88)( 29, 89)( 30,105)( 31,106)( 32,107)( 33,102)
( 34,103)( 35,104)( 36, 99)( 37,100)( 38,101)( 39, 96)( 40, 97)( 41, 98)
( 42, 93)( 43, 94)( 44, 95)( 45,111)( 46,112)( 47,113)( 48,108)( 49,109)
( 50,110)( 51,126)( 52,127)( 53,128)( 54,123)( 55,124)( 56,125)( 57,120)
( 58,121)( 59,122)( 60,117)( 61,118)( 62,119)( 63,114)( 64,115)( 65,116);
poly := sub<Sym(128)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, 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*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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