Polytope of Type {14,18}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,18}*504
Also Known As : {14,18|2}. if this polytope has another name.
Group : SmallGroup(504,59)
Rank : 3
Schlafli Type : {14,18}
Number of vertices, edges, etc : 14, 126, 18
Order of s0s1s2 : 126
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,18,2} of size 1008
Vertex Figure Of :
   {2,14,18} of size 1008
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {14,6}*168
   7-fold quotients : {2,18}*72
   9-fold quotients : {14,2}*56
   14-fold quotients : {2,9}*36
   18-fold quotients : {7,2}*28
   21-fold quotients : {2,6}*24
   42-fold quotients : {2,3}*12
   63-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14,36}*1008, {28,18}*1008a
   3-fold covers : {14,54}*1512, {42,18}*1512a, {42,18}*1512b
Irregular Quotients (of which this is a minimal cover):
   None.

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);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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(126)!(  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(126)!(  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(126)!(  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);
poly := sub<Sym(126)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, 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 >;
References : None.
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