Polytope of Type {102,6}

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

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

Permutation Representation (Magma) :

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

References : None.
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