Polytope of Type {14,18,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,18,2}*1008
if this polytope has a name.
Group : SmallGroup(1008,507)
Rank : 4
Schlafli Type : {14,18,2}
Number of vertices, edges, etc : 14, 126, 18, 2
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 : {14,6,2}*336
   7-fold quotients : {2,18,2}*144
   9-fold quotients : {14,2,2}*112
   14-fold quotients : {2,9,2}*72
   18-fold quotients : {7,2,2}*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 := (  4, 19)(  5, 20)(  6, 21)(  7, 16)(  8, 17)(  9, 18)( 10, 13)( 11, 14)
( 12, 15)( 25, 40)( 26, 41)( 27, 42)( 28, 37)( 29, 38)( 30, 39)( 31, 34)
( 32, 35)( 33, 36)( 46, 61)( 47, 62)( 48, 63)( 49, 58)( 50, 59)( 51, 60)
( 52, 55)( 53, 56)( 54, 57)( 67, 82)( 68, 83)( 69, 84)( 70, 79)( 71, 80)
( 72, 81)( 73, 76)( 74, 77)( 75, 78)( 88,103)( 89,104)( 90,105)( 91,100)
( 92,101)( 93,102)( 94, 97)( 95, 98)( 96, 99)(109,124)(110,125)(111,126)
(112,121)(113,122)(114,123)(115,118)(116,119)(117,120);;
s1 := (  1,  4)(  2,  6)(  3,  5)(  7, 19)(  8, 21)(  9, 20)( 10, 16)( 11, 18)
( 12, 17)( 14, 15)( 22, 47)( 23, 46)( 24, 48)( 25, 44)( 26, 43)( 27, 45)
( 28, 62)( 29, 61)( 30, 63)( 31, 59)( 32, 58)( 33, 60)( 34, 56)( 35, 55)
( 36, 57)( 37, 53)( 38, 52)( 39, 54)( 40, 50)( 41, 49)( 42, 51)( 64, 67)
( 65, 69)( 66, 68)( 70, 82)( 71, 84)( 72, 83)( 73, 79)( 74, 81)( 75, 80)
( 77, 78)( 85,110)( 86,109)( 87,111)( 88,107)( 89,106)( 90,108)( 91,125)
( 92,124)( 93,126)( 94,122)( 95,121)( 96,123)( 97,119)( 98,118)( 99,120)
(100,116)(101,115)(102,117)(103,113)(104,112)(105,114);;
s2 := (  1, 85)(  2, 87)(  3, 86)(  4, 88)(  5, 90)(  6, 89)(  7, 91)(  8, 93)
(  9, 92)( 10, 94)( 11, 96)( 12, 95)( 13, 97)( 14, 99)( 15, 98)( 16,100)
( 17,102)( 18,101)( 19,103)( 20,105)( 21,104)( 22, 64)( 23, 66)( 24, 65)
( 25, 67)( 26, 69)( 27, 68)( 28, 70)( 29, 72)( 30, 71)( 31, 73)( 32, 75)
( 33, 74)( 34, 76)( 35, 78)( 36, 77)( 37, 79)( 38, 81)( 39, 80)( 40, 82)
( 41, 84)( 42, 83)( 43,107)( 44,106)( 45,108)( 46,110)( 47,109)( 48,111)
( 49,113)( 50,112)( 51,114)( 52,116)( 53,115)( 54,117)( 55,119)( 56,118)
( 57,120)( 58,122)( 59,121)( 60,123)( 61,125)( 62,124)( 63,126);;
s3 := (127,128);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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)!(  4, 19)(  5, 20)(  6, 21)(  7, 16)(  8, 17)(  9, 18)( 10, 13)
( 11, 14)( 12, 15)( 25, 40)( 26, 41)( 27, 42)( 28, 37)( 29, 38)( 30, 39)
( 31, 34)( 32, 35)( 33, 36)( 46, 61)( 47, 62)( 48, 63)( 49, 58)( 50, 59)
( 51, 60)( 52, 55)( 53, 56)( 54, 57)( 67, 82)( 68, 83)( 69, 84)( 70, 79)
( 71, 80)( 72, 81)( 73, 76)( 74, 77)( 75, 78)( 88,103)( 89,104)( 90,105)
( 91,100)( 92,101)( 93,102)( 94, 97)( 95, 98)( 96, 99)(109,124)(110,125)
(111,126)(112,121)(113,122)(114,123)(115,118)(116,119)(117,120);
s1 := Sym(128)!(  1,  4)(  2,  6)(  3,  5)(  7, 19)(  8, 21)(  9, 20)( 10, 16)
( 11, 18)( 12, 17)( 14, 15)( 22, 47)( 23, 46)( 24, 48)( 25, 44)( 26, 43)
( 27, 45)( 28, 62)( 29, 61)( 30, 63)( 31, 59)( 32, 58)( 33, 60)( 34, 56)
( 35, 55)( 36, 57)( 37, 53)( 38, 52)( 39, 54)( 40, 50)( 41, 49)( 42, 51)
( 64, 67)( 65, 69)( 66, 68)( 70, 82)( 71, 84)( 72, 83)( 73, 79)( 74, 81)
( 75, 80)( 77, 78)( 85,110)( 86,109)( 87,111)( 88,107)( 89,106)( 90,108)
( 91,125)( 92,124)( 93,126)( 94,122)( 95,121)( 96,123)( 97,119)( 98,118)
( 99,120)(100,116)(101,115)(102,117)(103,113)(104,112)(105,114);
s2 := Sym(128)!(  1, 85)(  2, 87)(  3, 86)(  4, 88)(  5, 90)(  6, 89)(  7, 91)
(  8, 93)(  9, 92)( 10, 94)( 11, 96)( 12, 95)( 13, 97)( 14, 99)( 15, 98)
( 16,100)( 17,102)( 18,101)( 19,103)( 20,105)( 21,104)( 22, 64)( 23, 66)
( 24, 65)( 25, 67)( 26, 69)( 27, 68)( 28, 70)( 29, 72)( 30, 71)( 31, 73)
( 32, 75)( 33, 74)( 34, 76)( 35, 78)( 36, 77)( 37, 79)( 38, 81)( 39, 80)
( 40, 82)( 41, 84)( 42, 83)( 43,107)( 44,106)( 45,108)( 46,110)( 47,109)
( 48,111)( 49,113)( 50,112)( 51,114)( 52,116)( 53,115)( 54,117)( 55,119)
( 56,118)( 57,120)( 58,122)( 59,121)( 60,123)( 61,125)( 62,124)( 63,126);
s3 := Sym(128)!(127,128);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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 >;

to this polytope