Polytope of Type {19,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {19,38}*1444
if this polytope has a name.
Group : SmallGroup(1444,9)
Rank : 3
Schlafli Type : {19,38}
Number of vertices, edges, etc : 19, 361, 38
Order of s₀s₁s₂ : 38
Order of s₀s₁s₂s₁ : 38
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) :
   19-fold quotients : {19,2}*76
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 20,343)( 21,361)( 22,360)( 23,359)( 24,358)( 25,357)( 26,356)
( 27,355)( 28,354)( 29,353)( 30,352)( 31,351)( 32,350)( 33,349)( 34,348)
( 35,347)( 36,346)( 37,345)( 38,344)( 39,324)( 40,342)( 41,341)( 42,340)
( 43,339)( 44,338)( 45,337)( 46,336)( 47,335)( 48,334)( 49,333)( 50,332)
( 51,331)( 52,330)( 53,329)( 54,328)( 55,327)( 56,326)( 57,325)( 58,305)
( 59,323)( 60,322)( 61,321)( 62,320)( 63,319)( 64,318)( 65,317)( 66,316)
( 67,315)( 68,314)( 69,313)( 70,312)( 71,311)( 72,310)( 73,309)( 74,308)
( 75,307)( 76,306)( 77,286)( 78,304)( 79,303)( 80,302)( 81,301)( 82,300)
( 83,299)( 84,298)( 85,297)( 86,296)( 87,295)( 88,294)( 89,293)( 90,292)
( 91,291)( 92,290)( 93,289)( 94,288)( 95,287)( 96,267)( 97,285)( 98,284)
( 99,283)(100,282)(101,281)(102,280)(103,279)(104,278)(105,277)(106,276)
(107,275)(108,274)(109,273)(110,272)(111,271)(112,270)(113,269)(114,268)
(115,248)(116,266)(117,265)(118,264)(119,263)(120,262)(121,261)(122,260)
(123,259)(124,258)(125,257)(126,256)(127,255)(128,254)(129,253)(130,252)
(131,251)(132,250)(133,249)(134,229)(135,247)(136,246)(137,245)(138,244)
(139,243)(140,242)(141,241)(142,240)(143,239)(144,238)(145,237)(146,236)
(147,235)(148,234)(149,233)(150,232)(151,231)(152,230)(153,210)(154,228)
(155,227)(156,226)(157,225)(158,224)(159,223)(160,222)(161,221)(162,220)
(163,219)(164,218)(165,217)(166,216)(167,215)(168,214)(169,213)(170,212)
(171,211)(172,191)(173,209)(174,208)(175,207)(176,206)(177,205)(178,204)
(179,203)(180,202)(181,201)(182,200)(183,199)(184,198)(185,197)(186,196)
(187,195)(188,194)(189,193)(190,192);;
s1 := (  1, 21)(  2, 20)(  3, 38)(  4, 37)(  5, 36)(  6, 35)(  7, 34)(  8, 33)
(  9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 39,344)( 40,343)( 41,361)( 42,360)( 43,359)
( 44,358)( 45,357)( 46,356)( 47,355)( 48,354)( 49,353)( 50,352)( 51,351)
( 52,350)( 53,349)( 54,348)( 55,347)( 56,346)( 57,345)( 58,325)( 59,324)
( 60,342)( 61,341)( 62,340)( 63,339)( 64,338)( 65,337)( 66,336)( 67,335)
( 68,334)( 69,333)( 70,332)( 71,331)( 72,330)( 73,329)( 74,328)( 75,327)
( 76,326)( 77,306)( 78,305)( 79,323)( 80,322)( 81,321)( 82,320)( 83,319)
( 84,318)( 85,317)( 86,316)( 87,315)( 88,314)( 89,313)( 90,312)( 91,311)
( 92,310)( 93,309)( 94,308)( 95,307)( 96,287)( 97,286)( 98,304)( 99,303)
(100,302)(101,301)(102,300)(103,299)(104,298)(105,297)(106,296)(107,295)
(108,294)(109,293)(110,292)(111,291)(112,290)(113,289)(114,288)(115,268)
(116,267)(117,285)(118,284)(119,283)(120,282)(121,281)(122,280)(123,279)
(124,278)(125,277)(126,276)(127,275)(128,274)(129,273)(130,272)(131,271)
(132,270)(133,269)(134,249)(135,248)(136,266)(137,265)(138,264)(139,263)
(140,262)(141,261)(142,260)(143,259)(144,258)(145,257)(146,256)(147,255)
(148,254)(149,253)(150,252)(151,251)(152,250)(153,230)(154,229)(155,247)
(156,246)(157,245)(158,244)(159,243)(160,242)(161,241)(162,240)(163,239)
(164,238)(165,237)(166,236)(167,235)(168,234)(169,233)(170,232)(171,231)
(172,211)(173,210)(174,228)(175,227)(176,226)(177,225)(178,224)(179,223)
(180,222)(181,221)(182,220)(183,219)(184,218)(185,217)(186,216)(187,215)
(188,214)(189,213)(190,212)(191,192)(193,209)(194,208)(195,207)(196,206)
(197,205)(198,204)(199,203)(200,202);;
s2 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 45, 52)
( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)
( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)( 81, 92)
( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)( 99,112)
(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(116,133)(117,132)
(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(135,152)
(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)(143,144)
(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)
(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)(197,204)
(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)(215,224)
(216,223)(217,222)(218,221)(219,220)(230,247)(231,246)(232,245)(233,244)
(234,243)(235,242)(236,241)(237,240)(238,239)(249,266)(250,265)(251,264)
(252,263)(253,262)(254,261)(255,260)(256,259)(257,258)(268,285)(269,284)
(270,283)(271,282)(272,281)(273,280)(274,279)(275,278)(276,277)(287,304)
(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)
(306,323)(307,322)(308,321)(309,320)(310,319)(311,318)(312,317)(313,316)
(314,315)(325,342)(326,341)(327,340)(328,339)(329,338)(330,337)(331,336)
(332,335)(333,334)(344,361)(345,360)(346,359)(347,358)(348,357)(349,356)
(350,355)(351,354)(352,353);;
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, s2*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(361)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 20,343)( 21,361)( 22,360)( 23,359)( 24,358)( 25,357)
( 26,356)( 27,355)( 28,354)( 29,353)( 30,352)( 31,351)( 32,350)( 33,349)
( 34,348)( 35,347)( 36,346)( 37,345)( 38,344)( 39,324)( 40,342)( 41,341)
( 42,340)( 43,339)( 44,338)( 45,337)( 46,336)( 47,335)( 48,334)( 49,333)
( 50,332)( 51,331)( 52,330)( 53,329)( 54,328)( 55,327)( 56,326)( 57,325)
( 58,305)( 59,323)( 60,322)( 61,321)( 62,320)( 63,319)( 64,318)( 65,317)
( 66,316)( 67,315)( 68,314)( 69,313)( 70,312)( 71,311)( 72,310)( 73,309)
( 74,308)( 75,307)( 76,306)( 77,286)( 78,304)( 79,303)( 80,302)( 81,301)
( 82,300)( 83,299)( 84,298)( 85,297)( 86,296)( 87,295)( 88,294)( 89,293)
( 90,292)( 91,291)( 92,290)( 93,289)( 94,288)( 95,287)( 96,267)( 97,285)
( 98,284)( 99,283)(100,282)(101,281)(102,280)(103,279)(104,278)(105,277)
(106,276)(107,275)(108,274)(109,273)(110,272)(111,271)(112,270)(113,269)
(114,268)(115,248)(116,266)(117,265)(118,264)(119,263)(120,262)(121,261)
(122,260)(123,259)(124,258)(125,257)(126,256)(127,255)(128,254)(129,253)
(130,252)(131,251)(132,250)(133,249)(134,229)(135,247)(136,246)(137,245)
(138,244)(139,243)(140,242)(141,241)(142,240)(143,239)(144,238)(145,237)
(146,236)(147,235)(148,234)(149,233)(150,232)(151,231)(152,230)(153,210)
(154,228)(155,227)(156,226)(157,225)(158,224)(159,223)(160,222)(161,221)
(162,220)(163,219)(164,218)(165,217)(166,216)(167,215)(168,214)(169,213)
(170,212)(171,211)(172,191)(173,209)(174,208)(175,207)(176,206)(177,205)
(178,204)(179,203)(180,202)(181,201)(182,200)(183,199)(184,198)(185,197)
(186,196)(187,195)(188,194)(189,193)(190,192);
s1 := Sym(361)!(  1, 21)(  2, 20)(  3, 38)(  4, 37)(  5, 36)(  6, 35)(  7, 34)
(  8, 33)(  9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)
( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 39,344)( 40,343)( 41,361)( 42,360)
( 43,359)( 44,358)( 45,357)( 46,356)( 47,355)( 48,354)( 49,353)( 50,352)
( 51,351)( 52,350)( 53,349)( 54,348)( 55,347)( 56,346)( 57,345)( 58,325)
( 59,324)( 60,342)( 61,341)( 62,340)( 63,339)( 64,338)( 65,337)( 66,336)
( 67,335)( 68,334)( 69,333)( 70,332)( 71,331)( 72,330)( 73,329)( 74,328)
( 75,327)( 76,326)( 77,306)( 78,305)( 79,323)( 80,322)( 81,321)( 82,320)
( 83,319)( 84,318)( 85,317)( 86,316)( 87,315)( 88,314)( 89,313)( 90,312)
( 91,311)( 92,310)( 93,309)( 94,308)( 95,307)( 96,287)( 97,286)( 98,304)
( 99,303)(100,302)(101,301)(102,300)(103,299)(104,298)(105,297)(106,296)
(107,295)(108,294)(109,293)(110,292)(111,291)(112,290)(113,289)(114,288)
(115,268)(116,267)(117,285)(118,284)(119,283)(120,282)(121,281)(122,280)
(123,279)(124,278)(125,277)(126,276)(127,275)(128,274)(129,273)(130,272)
(131,271)(132,270)(133,269)(134,249)(135,248)(136,266)(137,265)(138,264)
(139,263)(140,262)(141,261)(142,260)(143,259)(144,258)(145,257)(146,256)
(147,255)(148,254)(149,253)(150,252)(151,251)(152,250)(153,230)(154,229)
(155,247)(156,246)(157,245)(158,244)(159,243)(160,242)(161,241)(162,240)
(163,239)(164,238)(165,237)(166,236)(167,235)(168,234)(169,233)(170,232)
(171,231)(172,211)(173,210)(174,228)(175,227)(176,226)(177,225)(178,224)
(179,223)(180,222)(181,221)(182,220)(183,219)(184,218)(185,217)(186,216)
(187,215)(188,214)(189,213)(190,212)(191,192)(193,209)(194,208)(195,207)
(196,206)(197,205)(198,204)(199,203)(200,202);
s2 := Sym(361)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)
( 27, 32)( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)
( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)
( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(116,133)
(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)
(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)
(143,144)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)
(161,164)(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)
(179,184)(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)
(197,204)(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)
(215,224)(216,223)(217,222)(218,221)(219,220)(230,247)(231,246)(232,245)
(233,244)(234,243)(235,242)(236,241)(237,240)(238,239)(249,266)(250,265)
(251,264)(252,263)(253,262)(254,261)(255,260)(256,259)(257,258)(268,285)
(269,284)(270,283)(271,282)(272,281)(273,280)(274,279)(275,278)(276,277)
(287,304)(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)
(295,296)(306,323)(307,322)(308,321)(309,320)(310,319)(311,318)(312,317)
(313,316)(314,315)(325,342)(326,341)(327,340)(328,339)(329,338)(330,337)
(331,336)(332,335)(333,334)(344,361)(345,360)(346,359)(347,358)(348,357)
(349,356)(350,355)(351,354)(352,353);
poly := sub<Sym(361)|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, s2*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope