Polytope of Type {102,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {102,6}*1836
if this polytope has a name.
Group : SmallGroup(1836,53)
Rank : 3
Schlafli Type : {102,6}
Number of vertices, edges, etc : 153, 459, 9
Order of s₀s₁s₂ : 51
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
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) :
   17-fold quotients : {6,6}*108
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope