Polytope of Type {6,102}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,102}*1224a
if this polytope has a name.
Group : SmallGroup(1224,139)
Rank : 3
Schlafli Type : {6,102}
Number of vertices, edges, etc : 6, 306, 102
Order of s₀s₁s₂ : 102
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {6,34}*408
   9-fold quotients : {2,34}*136
   17-fold quotients : {6,6}*72c
   18-fold quotients : {2,17}*68
   34-fold quotients : {3,6}*36
   51-fold quotients : {6,2}*24
   102-fold quotients : {3,2}*12
   153-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 18, 35)( 19, 36)( 20, 37)( 21, 38)( 22, 39)( 23, 40)( 24, 41)( 25, 42)
( 26, 43)( 27, 44)( 28, 45)( 29, 46)( 30, 47)( 31, 48)( 32, 49)( 33, 50)
( 34, 51)( 52,103)( 53,104)( 54,105)( 55,106)( 56,107)( 57,108)( 58,109)
( 59,110)( 60,111)( 61,112)( 62,113)( 63,114)( 64,115)( 65,116)( 66,117)
( 67,118)( 68,119)( 69,137)( 70,138)( 71,139)( 72,140)( 73,141)( 74,142)
( 75,143)( 76,144)( 77,145)( 78,146)( 79,147)( 80,148)( 81,149)( 82,150)
( 83,151)( 84,152)( 85,153)( 86,120)( 87,121)( 88,122)( 89,123)( 90,124)
( 91,125)( 92,126)( 93,127)( 94,128)( 95,129)( 96,130)( 97,131)( 98,132)
( 99,133)(100,134)(101,135)(102,136);;
s1 := (  1, 69)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 81)(  7, 80)(  8, 79)
(  9, 78)( 10, 77)( 11, 76)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 71)
( 17, 70)( 18, 52)( 19, 68)( 20, 67)( 21, 66)( 22, 65)( 23, 64)( 24, 63)
( 25, 62)( 26, 61)( 27, 60)( 28, 59)( 29, 58)( 30, 57)( 31, 56)( 32, 55)
( 33, 54)( 34, 53)( 35, 86)( 36,102)( 37,101)( 38,100)( 39, 99)( 40, 98)
( 41, 97)( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 91)( 48, 90)
( 49, 89)( 50, 88)( 51, 87)(103,120)(104,136)(105,135)(106,134)(107,133)
(108,132)(109,131)(110,130)(111,129)(112,128)(113,127)(114,126)(115,125)
(116,124)(117,123)(118,122)(119,121)(138,153)(139,152)(140,151)(141,150)
(142,149)(143,148)(144,147)(145,146);;
s2 := (  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)
( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)( 26, 28)
( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)
( 52,104)( 53,103)( 54,119)( 55,118)( 56,117)( 57,116)( 58,115)( 59,114)
( 60,113)( 61,112)( 62,111)( 63,110)( 64,109)( 65,108)( 66,107)( 67,106)
( 68,105)( 69,121)( 70,120)( 71,136)( 72,135)( 73,134)( 74,133)( 75,132)
( 76,131)( 77,130)( 78,129)( 79,128)( 80,127)( 81,126)( 82,125)( 83,124)
( 84,123)( 85,122)( 86,138)( 87,137)( 88,153)( 89,152)( 90,151)( 91,150)
( 92,149)( 93,148)( 94,147)( 95,146)( 96,145)( 97,144)( 98,143)( 99,142)
(100,141)(101,140)(102,139);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*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*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*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(153)!( 18, 35)( 19, 36)( 20, 37)( 21, 38)( 22, 39)( 23, 40)( 24, 41)
( 25, 42)( 26, 43)( 27, 44)( 28, 45)( 29, 46)( 30, 47)( 31, 48)( 32, 49)
( 33, 50)( 34, 51)( 52,103)( 53,104)( 54,105)( 55,106)( 56,107)( 57,108)
( 58,109)( 59,110)( 60,111)( 61,112)( 62,113)( 63,114)( 64,115)( 65,116)
( 66,117)( 67,118)( 68,119)( 69,137)( 70,138)( 71,139)( 72,140)( 73,141)
( 74,142)( 75,143)( 76,144)( 77,145)( 78,146)( 79,147)( 80,148)( 81,149)
( 82,150)( 83,151)( 84,152)( 85,153)( 86,120)( 87,121)( 88,122)( 89,123)
( 90,124)( 91,125)( 92,126)( 93,127)( 94,128)( 95,129)( 96,130)( 97,131)
( 98,132)( 99,133)(100,134)(101,135)(102,136);
s1 := Sym(153)!(  1, 69)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 81)(  7, 80)
(  8, 79)(  9, 78)( 10, 77)( 11, 76)( 12, 75)( 13, 74)( 14, 73)( 15, 72)
( 16, 71)( 17, 70)( 18, 52)( 19, 68)( 20, 67)( 21, 66)( 22, 65)( 23, 64)
( 24, 63)( 25, 62)( 26, 61)( 27, 60)( 28, 59)( 29, 58)( 30, 57)( 31, 56)
( 32, 55)( 33, 54)( 34, 53)( 35, 86)( 36,102)( 37,101)( 38,100)( 39, 99)
( 40, 98)( 41, 97)( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 91)
( 48, 90)( 49, 89)( 50, 88)( 51, 87)(103,120)(104,136)(105,135)(106,134)
(107,133)(108,132)(109,131)(110,130)(111,129)(112,128)(113,127)(114,126)
(115,125)(116,124)(117,123)(118,122)(119,121)(138,153)(139,152)(140,151)
(141,150)(142,149)(143,148)(144,147)(145,146);
s2 := Sym(153)!(  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)
(  9, 11)( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)
( 26, 28)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 43, 45)( 52,104)( 53,103)( 54,119)( 55,118)( 56,117)( 57,116)( 58,115)
( 59,114)( 60,113)( 61,112)( 62,111)( 63,110)( 64,109)( 65,108)( 66,107)
( 67,106)( 68,105)( 69,121)( 70,120)( 71,136)( 72,135)( 73,134)( 74,133)
( 75,132)( 76,131)( 77,130)( 78,129)( 79,128)( 80,127)( 81,126)( 82,125)
( 83,124)( 84,123)( 85,122)( 86,138)( 87,137)( 88,153)( 89,152)( 90,151)
( 91,150)( 92,149)( 93,148)( 94,147)( 95,146)( 96,145)( 97,144)( 98,143)
( 99,142)(100,141)(101,140)(102,139);
poly := sub<Sym(153)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*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*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*s0*s1*s2*s1 >;

References : None.
to this polytope