Polytope of Type {18,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,22}*792
Also Known As : {18,22|2}. if this polytope has another name.
Group : SmallGroup(792,40)
Rank : 3
Schlafli Type : {18,22}
Number of vertices, edges, etc : 18, 198, 22
Order of s₀s₁s₂ : 198
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {18,22,2} of size 1584
Vertex Figure Of :
   {2,18,22} of size 1584
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,22}*264
   9-fold quotients : {2,22}*88
   11-fold quotients : {18,2}*72
   18-fold quotients : {2,11}*44
   22-fold quotients : {9,2}*36
   33-fold quotients : {6,2}*24
   66-fold quotients : {3,2}*12
   99-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {36,22}*1584, {18,44}*1584a
Permutation Representation (GAP) :

s0 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 26, 27)( 29, 30)( 32, 33)( 34, 69)( 35, 68)( 36, 67)( 37, 72)( 38, 71)
( 39, 70)( 40, 75)( 41, 74)( 42, 73)( 43, 78)( 44, 77)( 45, 76)( 46, 81)
( 47, 80)( 48, 79)( 49, 84)( 50, 83)( 51, 82)( 52, 87)( 53, 86)( 54, 85)
( 55, 90)( 56, 89)( 57, 88)( 58, 93)( 59, 92)( 60, 91)( 61, 96)( 62, 95)
( 63, 94)( 64, 99)( 65, 98)( 66, 97)(101,102)(104,105)(107,108)(110,111)
(113,114)(116,117)(119,120)(122,123)(125,126)(128,129)(131,132)(133,168)
(134,167)(135,166)(136,171)(137,170)(138,169)(139,174)(140,173)(141,172)
(142,177)(143,176)(144,175)(145,180)(146,179)(147,178)(148,183)(149,182)
(150,181)(151,186)(152,185)(153,184)(154,189)(155,188)(156,187)(157,192)
(158,191)(159,190)(160,195)(161,194)(162,193)(163,198)(164,197)(165,196);;
s1 := (  1, 34)(  2, 36)(  3, 35)(  4, 64)(  5, 66)(  6, 65)(  7, 61)(  8, 63)
(  9, 62)( 10, 58)( 11, 60)( 12, 59)( 13, 55)( 14, 57)( 15, 56)( 16, 52)
( 17, 54)( 18, 53)( 19, 49)( 20, 51)( 21, 50)( 22, 46)( 23, 48)( 24, 47)
( 25, 43)( 26, 45)( 27, 44)( 28, 40)( 29, 42)( 30, 41)( 31, 37)( 32, 39)
( 33, 38)( 67, 69)( 70, 99)( 71, 98)( 72, 97)( 73, 96)( 74, 95)( 75, 94)
( 76, 93)( 77, 92)( 78, 91)( 79, 90)( 80, 89)( 81, 88)( 82, 87)( 83, 86)
( 84, 85)(100,133)(101,135)(102,134)(103,163)(104,165)(105,164)(106,160)
(107,162)(108,161)(109,157)(110,159)(111,158)(112,154)(113,156)(114,155)
(115,151)(116,153)(117,152)(118,148)(119,150)(120,149)(121,145)(122,147)
(123,146)(124,142)(125,144)(126,143)(127,139)(128,141)(129,140)(130,136)
(131,138)(132,137)(166,168)(169,198)(170,197)(171,196)(172,195)(173,194)
(174,193)(175,192)(176,191)(177,190)(178,189)(179,188)(180,187)(181,186)
(182,185)(183,184);;
s2 := (  1,103)(  2,104)(  3,105)(  4,100)(  5,101)(  6,102)(  7,130)(  8,131)
(  9,132)( 10,127)( 11,128)( 12,129)( 13,124)( 14,125)( 15,126)( 16,121)
( 17,122)( 18,123)( 19,118)( 20,119)( 21,120)( 22,115)( 23,116)( 24,117)
( 25,112)( 26,113)( 27,114)( 28,109)( 29,110)( 30,111)( 31,106)( 32,107)
( 33,108)( 34,136)( 35,137)( 36,138)( 37,133)( 38,134)( 39,135)( 40,163)
( 41,164)( 42,165)( 43,160)( 44,161)( 45,162)( 46,157)( 47,158)( 48,159)
( 49,154)( 50,155)( 51,156)( 52,151)( 53,152)( 54,153)( 55,148)( 56,149)
( 57,150)( 58,145)( 59,146)( 60,147)( 61,142)( 62,143)( 63,144)( 64,139)
( 65,140)( 66,141)( 67,169)( 68,170)( 69,171)( 70,166)( 71,167)( 72,168)
( 73,196)( 74,197)( 75,198)( 76,193)( 77,194)( 78,195)( 79,190)( 80,191)
( 81,192)( 82,187)( 83,188)( 84,189)( 85,184)( 86,185)( 87,186)( 88,181)
( 89,182)( 90,183)( 91,178)( 92,179)( 93,180)( 94,175)( 95,176)( 96,177)
( 97,172)( 98,173)( 99,174);;
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*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(198)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)
( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 34, 69)( 35, 68)( 36, 67)( 37, 72)
( 38, 71)( 39, 70)( 40, 75)( 41, 74)( 42, 73)( 43, 78)( 44, 77)( 45, 76)
( 46, 81)( 47, 80)( 48, 79)( 49, 84)( 50, 83)( 51, 82)( 52, 87)( 53, 86)
( 54, 85)( 55, 90)( 56, 89)( 57, 88)( 58, 93)( 59, 92)( 60, 91)( 61, 96)
( 62, 95)( 63, 94)( 64, 99)( 65, 98)( 66, 97)(101,102)(104,105)(107,108)
(110,111)(113,114)(116,117)(119,120)(122,123)(125,126)(128,129)(131,132)
(133,168)(134,167)(135,166)(136,171)(137,170)(138,169)(139,174)(140,173)
(141,172)(142,177)(143,176)(144,175)(145,180)(146,179)(147,178)(148,183)
(149,182)(150,181)(151,186)(152,185)(153,184)(154,189)(155,188)(156,187)
(157,192)(158,191)(159,190)(160,195)(161,194)(162,193)(163,198)(164,197)
(165,196);
s1 := Sym(198)!(  1, 34)(  2, 36)(  3, 35)(  4, 64)(  5, 66)(  6, 65)(  7, 61)
(  8, 63)(  9, 62)( 10, 58)( 11, 60)( 12, 59)( 13, 55)( 14, 57)( 15, 56)
( 16, 52)( 17, 54)( 18, 53)( 19, 49)( 20, 51)( 21, 50)( 22, 46)( 23, 48)
( 24, 47)( 25, 43)( 26, 45)( 27, 44)( 28, 40)( 29, 42)( 30, 41)( 31, 37)
( 32, 39)( 33, 38)( 67, 69)( 70, 99)( 71, 98)( 72, 97)( 73, 96)( 74, 95)
( 75, 94)( 76, 93)( 77, 92)( 78, 91)( 79, 90)( 80, 89)( 81, 88)( 82, 87)
( 83, 86)( 84, 85)(100,133)(101,135)(102,134)(103,163)(104,165)(105,164)
(106,160)(107,162)(108,161)(109,157)(110,159)(111,158)(112,154)(113,156)
(114,155)(115,151)(116,153)(117,152)(118,148)(119,150)(120,149)(121,145)
(122,147)(123,146)(124,142)(125,144)(126,143)(127,139)(128,141)(129,140)
(130,136)(131,138)(132,137)(166,168)(169,198)(170,197)(171,196)(172,195)
(173,194)(174,193)(175,192)(176,191)(177,190)(178,189)(179,188)(180,187)
(181,186)(182,185)(183,184);
s2 := Sym(198)!(  1,103)(  2,104)(  3,105)(  4,100)(  5,101)(  6,102)(  7,130)
(  8,131)(  9,132)( 10,127)( 11,128)( 12,129)( 13,124)( 14,125)( 15,126)
( 16,121)( 17,122)( 18,123)( 19,118)( 20,119)( 21,120)( 22,115)( 23,116)
( 24,117)( 25,112)( 26,113)( 27,114)( 28,109)( 29,110)( 30,111)( 31,106)
( 32,107)( 33,108)( 34,136)( 35,137)( 36,138)( 37,133)( 38,134)( 39,135)
( 40,163)( 41,164)( 42,165)( 43,160)( 44,161)( 45,162)( 46,157)( 47,158)
( 48,159)( 49,154)( 50,155)( 51,156)( 52,151)( 53,152)( 54,153)( 55,148)
( 56,149)( 57,150)( 58,145)( 59,146)( 60,147)( 61,142)( 62,143)( 63,144)
( 64,139)( 65,140)( 66,141)( 67,169)( 68,170)( 69,171)( 70,166)( 71,167)
( 72,168)( 73,196)( 74,197)( 75,198)( 76,193)( 77,194)( 78,195)( 79,190)
( 80,191)( 81,192)( 82,187)( 83,188)( 84,189)( 85,184)( 86,185)( 87,186)
( 88,181)( 89,182)( 90,183)( 91,178)( 92,179)( 93,180)( 94,175)( 95,176)
( 96,177)( 97,172)( 98,173)( 99,174);
poly := sub<Sym(198)|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*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*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope