Polytope of Type {38,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,18}*1368
Also Known As : {38,18|2}. if this polytope has another name.
Group : SmallGroup(1368,59)
Rank : 3
Schlafli Type : {38,18}
Number of vertices, edges, etc : 38, 342, 18
Order of s₀s₁s₂ : 342
Order of s₀s₁s₂s₁ : 2
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 : {38,6}*456
   9-fold quotients : {38,2}*152
   18-fold quotients : {19,2}*76
   19-fold quotients : {2,18}*72
   38-fold quotients : {2,9}*36
   57-fold quotients : {2,6}*24
   114-fold quotients : {2,3}*12
   171-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  4, 55)(  5, 56)(  6, 57)(  7, 52)(  8, 53)(  9, 54)( 10, 49)( 11, 50)
( 12, 51)( 13, 46)( 14, 47)( 15, 48)( 16, 43)( 17, 44)( 18, 45)( 19, 40)
( 20, 41)( 21, 42)( 22, 37)( 23, 38)( 24, 39)( 25, 34)( 26, 35)( 27, 36)
( 28, 31)( 29, 32)( 30, 33)( 61,112)( 62,113)( 63,114)( 64,109)( 65,110)
( 66,111)( 67,106)( 68,107)( 69,108)( 70,103)( 71,104)( 72,105)( 73,100)
( 74,101)( 75,102)( 76, 97)( 77, 98)( 78, 99)( 79, 94)( 80, 95)( 81, 96)
( 82, 91)( 83, 92)( 84, 93)( 85, 88)( 86, 89)( 87, 90)(118,169)(119,170)
(120,171)(121,166)(122,167)(123,168)(124,163)(125,164)(126,165)(127,160)
(128,161)(129,162)(130,157)(131,158)(132,159)(133,154)(134,155)(135,156)
(136,151)(137,152)(138,153)(139,148)(140,149)(141,150)(142,145)(143,146)
(144,147)(175,226)(176,227)(177,228)(178,223)(179,224)(180,225)(181,220)
(182,221)(183,222)(184,217)(185,218)(186,219)(187,214)(188,215)(189,216)
(190,211)(191,212)(192,213)(193,208)(194,209)(195,210)(196,205)(197,206)
(198,207)(199,202)(200,203)(201,204)(232,283)(233,284)(234,285)(235,280)
(236,281)(237,282)(238,277)(239,278)(240,279)(241,274)(242,275)(243,276)
(244,271)(245,272)(246,273)(247,268)(248,269)(249,270)(250,265)(251,266)
(252,267)(253,262)(254,263)(255,264)(256,259)(257,260)(258,261)(289,340)
(290,341)(291,342)(292,337)(293,338)(294,339)(295,334)(296,335)(297,336)
(298,331)(299,332)(300,333)(301,328)(302,329)(303,330)(304,325)(305,326)
(306,327)(307,322)(308,323)(309,324)(310,319)(311,320)(312,321)(313,316)
(314,317)(315,318);;
s1 := (  1,  4)(  2,  6)(  3,  5)(  7, 55)(  8, 57)(  9, 56)( 10, 52)( 11, 54)
( 12, 53)( 13, 49)( 14, 51)( 15, 50)( 16, 46)( 17, 48)( 18, 47)( 19, 43)
( 20, 45)( 21, 44)( 22, 40)( 23, 42)( 24, 41)( 25, 37)( 26, 39)( 27, 38)
( 28, 34)( 29, 36)( 30, 35)( 32, 33)( 58,119)( 59,118)( 60,120)( 61,116)
( 62,115)( 63,117)( 64,170)( 65,169)( 66,171)( 67,167)( 68,166)( 69,168)
( 70,164)( 71,163)( 72,165)( 73,161)( 74,160)( 75,162)( 76,158)( 77,157)
( 78,159)( 79,155)( 80,154)( 81,156)( 82,152)( 83,151)( 84,153)( 85,149)
( 86,148)( 87,150)( 88,146)( 89,145)( 90,147)( 91,143)( 92,142)( 93,144)
( 94,140)( 95,139)( 96,141)( 97,137)( 98,136)( 99,138)(100,134)(101,133)
(102,135)(103,131)(104,130)(105,132)(106,128)(107,127)(108,129)(109,125)
(110,124)(111,126)(112,122)(113,121)(114,123)(172,175)(173,177)(174,176)
(178,226)(179,228)(180,227)(181,223)(182,225)(183,224)(184,220)(185,222)
(186,221)(187,217)(188,219)(189,218)(190,214)(191,216)(192,215)(193,211)
(194,213)(195,212)(196,208)(197,210)(198,209)(199,205)(200,207)(201,206)
(203,204)(229,290)(230,289)(231,291)(232,287)(233,286)(234,288)(235,341)
(236,340)(237,342)(238,338)(239,337)(240,339)(241,335)(242,334)(243,336)
(244,332)(245,331)(246,333)(247,329)(248,328)(249,330)(250,326)(251,325)
(252,327)(253,323)(254,322)(255,324)(256,320)(257,319)(258,321)(259,317)
(260,316)(261,318)(262,314)(263,313)(264,315)(265,311)(266,310)(267,312)
(268,308)(269,307)(270,309)(271,305)(272,304)(273,306)(274,302)(275,301)
(276,303)(277,299)(278,298)(279,300)(280,296)(281,295)(282,297)(283,293)
(284,292)(285,294);;
s2 := (  1,229)(  2,231)(  3,230)(  4,232)(  5,234)(  6,233)(  7,235)(  8,237)
(  9,236)( 10,238)( 11,240)( 12,239)( 13,241)( 14,243)( 15,242)( 16,244)
( 17,246)( 18,245)( 19,247)( 20,249)( 21,248)( 22,250)( 23,252)( 24,251)
( 25,253)( 26,255)( 27,254)( 28,256)( 29,258)( 30,257)( 31,259)( 32,261)
( 33,260)( 34,262)( 35,264)( 36,263)( 37,265)( 38,267)( 39,266)( 40,268)
( 41,270)( 42,269)( 43,271)( 44,273)( 45,272)( 46,274)( 47,276)( 48,275)
( 49,277)( 50,279)( 51,278)( 52,280)( 53,282)( 54,281)( 55,283)( 56,285)
( 57,284)( 58,172)( 59,174)( 60,173)( 61,175)( 62,177)( 63,176)( 64,178)
( 65,180)( 66,179)( 67,181)( 68,183)( 69,182)( 70,184)( 71,186)( 72,185)
( 73,187)( 74,189)( 75,188)( 76,190)( 77,192)( 78,191)( 79,193)( 80,195)
( 81,194)( 82,196)( 83,198)( 84,197)( 85,199)( 86,201)( 87,200)( 88,202)
( 89,204)( 90,203)( 91,205)( 92,207)( 93,206)( 94,208)( 95,210)( 96,209)
( 97,211)( 98,213)( 99,212)(100,214)(101,216)(102,215)(103,217)(104,219)
(105,218)(106,220)(107,222)(108,221)(109,223)(110,225)(111,224)(112,226)
(113,228)(114,227)(115,287)(116,286)(117,288)(118,290)(119,289)(120,291)
(121,293)(122,292)(123,294)(124,296)(125,295)(126,297)(127,299)(128,298)
(129,300)(130,302)(131,301)(132,303)(133,305)(134,304)(135,306)(136,308)
(137,307)(138,309)(139,311)(140,310)(141,312)(142,314)(143,313)(144,315)
(145,317)(146,316)(147,318)(148,320)(149,319)(150,321)(151,323)(152,322)
(153,324)(154,326)(155,325)(156,327)(157,329)(158,328)(159,330)(160,332)
(161,331)(162,333)(163,335)(164,334)(165,336)(166,338)(167,337)(168,339)
(169,341)(170,340)(171,342);;
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, 
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*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*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(342)!(  4, 55)(  5, 56)(  6, 57)(  7, 52)(  8, 53)(  9, 54)( 10, 49)
( 11, 50)( 12, 51)( 13, 46)( 14, 47)( 15, 48)( 16, 43)( 17, 44)( 18, 45)
( 19, 40)( 20, 41)( 21, 42)( 22, 37)( 23, 38)( 24, 39)( 25, 34)( 26, 35)
( 27, 36)( 28, 31)( 29, 32)( 30, 33)( 61,112)( 62,113)( 63,114)( 64,109)
( 65,110)( 66,111)( 67,106)( 68,107)( 69,108)( 70,103)( 71,104)( 72,105)
( 73,100)( 74,101)( 75,102)( 76, 97)( 77, 98)( 78, 99)( 79, 94)( 80, 95)
( 81, 96)( 82, 91)( 83, 92)( 84, 93)( 85, 88)( 86, 89)( 87, 90)(118,169)
(119,170)(120,171)(121,166)(122,167)(123,168)(124,163)(125,164)(126,165)
(127,160)(128,161)(129,162)(130,157)(131,158)(132,159)(133,154)(134,155)
(135,156)(136,151)(137,152)(138,153)(139,148)(140,149)(141,150)(142,145)
(143,146)(144,147)(175,226)(176,227)(177,228)(178,223)(179,224)(180,225)
(181,220)(182,221)(183,222)(184,217)(185,218)(186,219)(187,214)(188,215)
(189,216)(190,211)(191,212)(192,213)(193,208)(194,209)(195,210)(196,205)
(197,206)(198,207)(199,202)(200,203)(201,204)(232,283)(233,284)(234,285)
(235,280)(236,281)(237,282)(238,277)(239,278)(240,279)(241,274)(242,275)
(243,276)(244,271)(245,272)(246,273)(247,268)(248,269)(249,270)(250,265)
(251,266)(252,267)(253,262)(254,263)(255,264)(256,259)(257,260)(258,261)
(289,340)(290,341)(291,342)(292,337)(293,338)(294,339)(295,334)(296,335)
(297,336)(298,331)(299,332)(300,333)(301,328)(302,329)(303,330)(304,325)
(305,326)(306,327)(307,322)(308,323)(309,324)(310,319)(311,320)(312,321)
(313,316)(314,317)(315,318);
s1 := Sym(342)!(  1,  4)(  2,  6)(  3,  5)(  7, 55)(  8, 57)(  9, 56)( 10, 52)
( 11, 54)( 12, 53)( 13, 49)( 14, 51)( 15, 50)( 16, 46)( 17, 48)( 18, 47)
( 19, 43)( 20, 45)( 21, 44)( 22, 40)( 23, 42)( 24, 41)( 25, 37)( 26, 39)
( 27, 38)( 28, 34)( 29, 36)( 30, 35)( 32, 33)( 58,119)( 59,118)( 60,120)
( 61,116)( 62,115)( 63,117)( 64,170)( 65,169)( 66,171)( 67,167)( 68,166)
( 69,168)( 70,164)( 71,163)( 72,165)( 73,161)( 74,160)( 75,162)( 76,158)
( 77,157)( 78,159)( 79,155)( 80,154)( 81,156)( 82,152)( 83,151)( 84,153)
( 85,149)( 86,148)( 87,150)( 88,146)( 89,145)( 90,147)( 91,143)( 92,142)
( 93,144)( 94,140)( 95,139)( 96,141)( 97,137)( 98,136)( 99,138)(100,134)
(101,133)(102,135)(103,131)(104,130)(105,132)(106,128)(107,127)(108,129)
(109,125)(110,124)(111,126)(112,122)(113,121)(114,123)(172,175)(173,177)
(174,176)(178,226)(179,228)(180,227)(181,223)(182,225)(183,224)(184,220)
(185,222)(186,221)(187,217)(188,219)(189,218)(190,214)(191,216)(192,215)
(193,211)(194,213)(195,212)(196,208)(197,210)(198,209)(199,205)(200,207)
(201,206)(203,204)(229,290)(230,289)(231,291)(232,287)(233,286)(234,288)
(235,341)(236,340)(237,342)(238,338)(239,337)(240,339)(241,335)(242,334)
(243,336)(244,332)(245,331)(246,333)(247,329)(248,328)(249,330)(250,326)
(251,325)(252,327)(253,323)(254,322)(255,324)(256,320)(257,319)(258,321)
(259,317)(260,316)(261,318)(262,314)(263,313)(264,315)(265,311)(266,310)
(267,312)(268,308)(269,307)(270,309)(271,305)(272,304)(273,306)(274,302)
(275,301)(276,303)(277,299)(278,298)(279,300)(280,296)(281,295)(282,297)
(283,293)(284,292)(285,294);
s2 := Sym(342)!(  1,229)(  2,231)(  3,230)(  4,232)(  5,234)(  6,233)(  7,235)
(  8,237)(  9,236)( 10,238)( 11,240)( 12,239)( 13,241)( 14,243)( 15,242)
( 16,244)( 17,246)( 18,245)( 19,247)( 20,249)( 21,248)( 22,250)( 23,252)
( 24,251)( 25,253)( 26,255)( 27,254)( 28,256)( 29,258)( 30,257)( 31,259)
( 32,261)( 33,260)( 34,262)( 35,264)( 36,263)( 37,265)( 38,267)( 39,266)
( 40,268)( 41,270)( 42,269)( 43,271)( 44,273)( 45,272)( 46,274)( 47,276)
( 48,275)( 49,277)( 50,279)( 51,278)( 52,280)( 53,282)( 54,281)( 55,283)
( 56,285)( 57,284)( 58,172)( 59,174)( 60,173)( 61,175)( 62,177)( 63,176)
( 64,178)( 65,180)( 66,179)( 67,181)( 68,183)( 69,182)( 70,184)( 71,186)
( 72,185)( 73,187)( 74,189)( 75,188)( 76,190)( 77,192)( 78,191)( 79,193)
( 80,195)( 81,194)( 82,196)( 83,198)( 84,197)( 85,199)( 86,201)( 87,200)
( 88,202)( 89,204)( 90,203)( 91,205)( 92,207)( 93,206)( 94,208)( 95,210)
( 96,209)( 97,211)( 98,213)( 99,212)(100,214)(101,216)(102,215)(103,217)
(104,219)(105,218)(106,220)(107,222)(108,221)(109,223)(110,225)(111,224)
(112,226)(113,228)(114,227)(115,287)(116,286)(117,288)(118,290)(119,289)
(120,291)(121,293)(122,292)(123,294)(124,296)(125,295)(126,297)(127,299)
(128,298)(129,300)(130,302)(131,301)(132,303)(133,305)(134,304)(135,306)
(136,308)(137,307)(138,309)(139,311)(140,310)(141,312)(142,314)(143,313)
(144,315)(145,317)(146,316)(147,318)(148,320)(149,319)(150,321)(151,323)
(152,322)(153,324)(154,326)(155,325)(156,327)(157,329)(158,328)(159,330)
(160,332)(161,331)(162,333)(163,335)(164,334)(165,336)(166,338)(167,337)
(168,339)(169,341)(170,340)(171,342);
poly := sub<Sym(342)|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, 
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*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*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