Polytope of Type {38,19}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,19}*1444
if this polytope has a name.
Group : SmallGroup(1444,9)
Rank : 3
Schlafli Type : {38,19}
Number of vertices, edges, etc : 38, 361, 19
Order of s₀s₁s₂ : 38
Order of s₀s₁s₂s₁ : 38
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) :
   19-fold quotients : {2,19}*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)( 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);;
s1 := (  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)(  9, 13)
( 10, 12)( 20,344)( 21,343)( 22,361)( 23,360)( 24,359)( 25,358)( 26,357)
( 27,356)( 28,355)( 29,354)( 30,353)( 31,352)( 32,351)( 33,350)( 34,349)
( 35,348)( 36,347)( 37,346)( 38,345)( 39,325)( 40,324)( 41,342)( 42,341)
( 43,340)( 44,339)( 45,338)( 46,337)( 47,336)( 48,335)( 49,334)( 50,333)
( 51,332)( 52,331)( 53,330)( 54,329)( 55,328)( 56,327)( 57,326)( 58,306)
( 59,305)( 60,323)( 61,322)( 62,321)( 63,320)( 64,319)( 65,318)( 66,317)
( 67,316)( 68,315)( 69,314)( 70,313)( 71,312)( 72,311)( 73,310)( 74,309)
( 75,308)( 76,307)( 77,287)( 78,286)( 79,304)( 80,303)( 81,302)( 82,301)
( 83,300)( 84,299)( 85,298)( 86,297)( 87,296)( 88,295)( 89,294)( 90,293)
( 91,292)( 92,291)( 93,290)( 94,289)( 95,288)( 96,268)( 97,267)( 98,285)
( 99,284)(100,283)(101,282)(102,281)(103,280)(104,279)(105,278)(106,277)
(107,276)(108,275)(109,274)(110,273)(111,272)(112,271)(113,270)(114,269)
(115,249)(116,248)(117,266)(118,265)(119,264)(120,263)(121,262)(122,261)
(123,260)(124,259)(125,258)(126,257)(127,256)(128,255)(129,254)(130,253)
(131,252)(132,251)(133,250)(134,230)(135,229)(136,247)(137,246)(138,245)
(139,244)(140,243)(141,242)(142,241)(143,240)(144,239)(145,238)(146,237)
(147,236)(148,235)(149,234)(150,233)(151,232)(152,231)(153,211)(154,210)
(155,228)(156,227)(157,226)(158,225)(159,224)(160,223)(161,222)(162,221)
(163,220)(164,219)(165,218)(166,217)(167,216)(168,215)(169,214)(170,213)
(171,212)(172,192)(173,191)(174,209)(175,208)(176,207)(177,206)(178,205)
(179,204)(180,203)(181,202)(182,201)(183,200)(184,199)(185,198)(186,197)
(187,196)(188,195)(189,194)(190,193);;
s2 := (  1, 20)(  2, 38)(  3, 37)(  4, 36)(  5, 35)(  6, 34)(  7, 33)(  8, 32)
(  9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)( 16, 24)
( 17, 23)( 18, 22)( 19, 21)( 39,343)( 40,361)( 41,360)( 42,359)( 43,358)
( 44,357)( 45,356)( 46,355)( 47,354)( 48,353)( 49,352)( 50,351)( 51,350)
( 52,349)( 53,348)( 54,347)( 55,346)( 56,345)( 57,344)( 58,324)( 59,342)
( 60,341)( 61,340)( 62,339)( 63,338)( 64,337)( 65,336)( 66,335)( 67,334)
( 68,333)( 69,332)( 70,331)( 71,330)( 72,329)( 73,328)( 74,327)( 75,326)
( 76,325)( 77,305)( 78,323)( 79,322)( 80,321)( 81,320)( 82,319)( 83,318)
( 84,317)( 85,316)( 86,315)( 87,314)( 88,313)( 89,312)( 90,311)( 91,310)
( 92,309)( 93,308)( 94,307)( 95,306)( 96,286)( 97,304)( 98,303)( 99,302)
(100,301)(101,300)(102,299)(103,298)(104,297)(105,296)(106,295)(107,294)
(108,293)(109,292)(110,291)(111,290)(112,289)(113,288)(114,287)(115,267)
(116,285)(117,284)(118,283)(119,282)(120,281)(121,280)(122,279)(123,278)
(124,277)(125,276)(126,275)(127,274)(128,273)(129,272)(130,271)(131,270)
(132,269)(133,268)(134,248)(135,266)(136,265)(137,264)(138,263)(139,262)
(140,261)(141,260)(142,259)(143,258)(144,257)(145,256)(146,255)(147,254)
(148,253)(149,252)(150,251)(151,250)(152,249)(153,229)(154,247)(155,246)
(156,245)(157,244)(158,243)(159,242)(160,241)(161,240)(162,239)(163,238)
(164,237)(165,236)(166,235)(167,234)(168,233)(169,232)(170,231)(171,230)
(172,210)(173,228)(174,227)(175,226)(176,225)(177,224)(178,223)(179,222)
(180,221)(181,220)(182,219)(183,218)(184,217)(185,216)(186,215)(187,214)
(188,213)(189,212)(190,211)(192,209)(193,208)(194,207)(195,206)(196,205)
(197,204)(198,203)(199,202)(200,201);;
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*s0*s1*s2*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 ];;
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)( 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);
s1 := Sym(361)!(  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)
(  9, 13)( 10, 12)( 20,344)( 21,343)( 22,361)( 23,360)( 24,359)( 25,358)
( 26,357)( 27,356)( 28,355)( 29,354)( 30,353)( 31,352)( 32,351)( 33,350)
( 34,349)( 35,348)( 36,347)( 37,346)( 38,345)( 39,325)( 40,324)( 41,342)
( 42,341)( 43,340)( 44,339)( 45,338)( 46,337)( 47,336)( 48,335)( 49,334)
( 50,333)( 51,332)( 52,331)( 53,330)( 54,329)( 55,328)( 56,327)( 57,326)
( 58,306)( 59,305)( 60,323)( 61,322)( 62,321)( 63,320)( 64,319)( 65,318)
( 66,317)( 67,316)( 68,315)( 69,314)( 70,313)( 71,312)( 72,311)( 73,310)
( 74,309)( 75,308)( 76,307)( 77,287)( 78,286)( 79,304)( 80,303)( 81,302)
( 82,301)( 83,300)( 84,299)( 85,298)( 86,297)( 87,296)( 88,295)( 89,294)
( 90,293)( 91,292)( 92,291)( 93,290)( 94,289)( 95,288)( 96,268)( 97,267)
( 98,285)( 99,284)(100,283)(101,282)(102,281)(103,280)(104,279)(105,278)
(106,277)(107,276)(108,275)(109,274)(110,273)(111,272)(112,271)(113,270)
(114,269)(115,249)(116,248)(117,266)(118,265)(119,264)(120,263)(121,262)
(122,261)(123,260)(124,259)(125,258)(126,257)(127,256)(128,255)(129,254)
(130,253)(131,252)(132,251)(133,250)(134,230)(135,229)(136,247)(137,246)
(138,245)(139,244)(140,243)(141,242)(142,241)(143,240)(144,239)(145,238)
(146,237)(147,236)(148,235)(149,234)(150,233)(151,232)(152,231)(153,211)
(154,210)(155,228)(156,227)(157,226)(158,225)(159,224)(160,223)(161,222)
(162,221)(163,220)(164,219)(165,218)(166,217)(167,216)(168,215)(169,214)
(170,213)(171,212)(172,192)(173,191)(174,209)(175,208)(176,207)(177,206)
(178,205)(179,204)(180,203)(181,202)(182,201)(183,200)(184,199)(185,198)
(186,197)(187,196)(188,195)(189,194)(190,193);
s2 := Sym(361)!(  1, 20)(  2, 38)(  3, 37)(  4, 36)(  5, 35)(  6, 34)(  7, 33)
(  8, 32)(  9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)
( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 39,343)( 40,361)( 41,360)( 42,359)
( 43,358)( 44,357)( 45,356)( 46,355)( 47,354)( 48,353)( 49,352)( 50,351)
( 51,350)( 52,349)( 53,348)( 54,347)( 55,346)( 56,345)( 57,344)( 58,324)
( 59,342)( 60,341)( 61,340)( 62,339)( 63,338)( 64,337)( 65,336)( 66,335)
( 67,334)( 68,333)( 69,332)( 70,331)( 71,330)( 72,329)( 73,328)( 74,327)
( 75,326)( 76,325)( 77,305)( 78,323)( 79,322)( 80,321)( 81,320)( 82,319)
( 83,318)( 84,317)( 85,316)( 86,315)( 87,314)( 88,313)( 89,312)( 90,311)
( 91,310)( 92,309)( 93,308)( 94,307)( 95,306)( 96,286)( 97,304)( 98,303)
( 99,302)(100,301)(101,300)(102,299)(103,298)(104,297)(105,296)(106,295)
(107,294)(108,293)(109,292)(110,291)(111,290)(112,289)(113,288)(114,287)
(115,267)(116,285)(117,284)(118,283)(119,282)(120,281)(121,280)(122,279)
(123,278)(124,277)(125,276)(126,275)(127,274)(128,273)(129,272)(130,271)
(131,270)(132,269)(133,268)(134,248)(135,266)(136,265)(137,264)(138,263)
(139,262)(140,261)(141,260)(142,259)(143,258)(144,257)(145,256)(146,255)
(147,254)(148,253)(149,252)(150,251)(151,250)(152,249)(153,229)(154,247)
(155,246)(156,245)(157,244)(158,243)(159,242)(160,241)(161,240)(162,239)
(163,238)(164,237)(165,236)(166,235)(167,234)(168,233)(169,232)(170,231)
(171,230)(172,210)(173,228)(174,227)(175,226)(176,225)(177,224)(178,223)
(179,222)(180,221)(181,220)(182,219)(183,218)(184,217)(185,216)(186,215)
(187,214)(188,213)(189,212)(190,211)(192,209)(193,208)(194,207)(195,206)
(196,205)(197,204)(198,203)(199,202)(200,201);
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*s0*s1*s2*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 >;

References : None.
to this polytope