Polytope of Type {20,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,38}*1520
Also Known As : {20,38|2}. if this polytope has another name.
Group : SmallGroup(1520,120)
Rank : 3
Schlafli Type : {20,38}
Number of vertices, edges, etc : 20, 380, 38
Order of s₀s₁s₂ : 380
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) :
   2-fold quotients : {10,38}*760
   5-fold quotients : {4,38}*304
   10-fold quotients : {2,38}*152
   19-fold quotients : {20,2}*80
   20-fold quotients : {2,19}*76
   38-fold quotients : {10,2}*40
   76-fold quotients : {5,2}*20
   95-fold quotients : {4,2}*16
   190-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 20, 77)( 21, 78)( 22, 79)( 23, 80)( 24, 81)( 25, 82)( 26, 83)( 27, 84)
( 28, 85)( 29, 86)( 30, 87)( 31, 88)( 32, 89)( 33, 90)( 34, 91)( 35, 92)
( 36, 93)( 37, 94)( 38, 95)( 39, 58)( 40, 59)( 41, 60)( 42, 61)( 43, 62)
( 44, 63)( 45, 64)( 46, 65)( 47, 66)( 48, 67)( 49, 68)( 50, 69)( 51, 70)
( 52, 71)( 53, 72)( 54, 73)( 55, 74)( 56, 75)( 57, 76)(115,172)(116,173)
(117,174)(118,175)(119,176)(120,177)(121,178)(122,179)(123,180)(124,181)
(125,182)(126,183)(127,184)(128,185)(129,186)(130,187)(131,188)(132,189)
(133,190)(134,153)(135,154)(136,155)(137,156)(138,157)(139,158)(140,159)
(141,160)(142,161)(143,162)(144,163)(145,164)(146,165)(147,166)(148,167)
(149,168)(150,169)(151,170)(152,171)(191,286)(192,287)(193,288)(194,289)
(195,290)(196,291)(197,292)(198,293)(199,294)(200,295)(201,296)(202,297)
(203,298)(204,299)(205,300)(206,301)(207,302)(208,303)(209,304)(210,362)
(211,363)(212,364)(213,365)(214,366)(215,367)(216,368)(217,369)(218,370)
(219,371)(220,372)(221,373)(222,374)(223,375)(224,376)(225,377)(226,378)
(227,379)(228,380)(229,343)(230,344)(231,345)(232,346)(233,347)(234,348)
(235,349)(236,350)(237,351)(238,352)(239,353)(240,354)(241,355)(242,356)
(243,357)(244,358)(245,359)(246,360)(247,361)(248,324)(249,325)(250,326)
(251,327)(252,328)(253,329)(254,330)(255,331)(256,332)(257,333)(258,334)
(259,335)(260,336)(261,337)(262,338)(263,339)(264,340)(265,341)(266,342)
(267,305)(268,306)(269,307)(270,308)(271,309)(272,310)(273,311)(274,312)
(275,313)(276,314)(277,315)(278,316)(279,317)(280,318)(281,319)(282,320)
(283,321)(284,322)(285,323);;
s1 := (  1,210)(  2,228)(  3,227)(  4,226)(  5,225)(  6,224)(  7,223)(  8,222)
(  9,221)( 10,220)( 11,219)( 12,218)( 13,217)( 14,216)( 15,215)( 16,214)
( 17,213)( 18,212)( 19,211)( 20,191)( 21,209)( 22,208)( 23,207)( 24,206)
( 25,205)( 26,204)( 27,203)( 28,202)( 29,201)( 30,200)( 31,199)( 32,198)
( 33,197)( 34,196)( 35,195)( 36,194)( 37,193)( 38,192)( 39,267)( 40,285)
( 41,284)( 42,283)( 43,282)( 44,281)( 45,280)( 46,279)( 47,278)( 48,277)
( 49,276)( 50,275)( 51,274)( 52,273)( 53,272)( 54,271)( 55,270)( 56,269)
( 57,268)( 58,248)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)( 64,261)
( 65,260)( 66,259)( 67,258)( 68,257)( 69,256)( 70,255)( 71,254)( 72,253)
( 73,252)( 74,251)( 75,250)( 76,249)( 77,229)( 78,247)( 79,246)( 80,245)
( 81,244)( 82,243)( 83,242)( 84,241)( 85,240)( 86,239)( 87,238)( 88,237)
( 89,236)( 90,235)( 91,234)( 92,233)( 93,232)( 94,231)( 95,230)( 96,305)
( 97,323)( 98,322)( 99,321)(100,320)(101,319)(102,318)(103,317)(104,316)
(105,315)(106,314)(107,313)(108,312)(109,311)(110,310)(111,309)(112,308)
(113,307)(114,306)(115,286)(116,304)(117,303)(118,302)(119,301)(120,300)
(121,299)(122,298)(123,297)(124,296)(125,295)(126,294)(127,293)(128,292)
(129,291)(130,290)(131,289)(132,288)(133,287)(134,362)(135,380)(136,379)
(137,378)(138,377)(139,376)(140,375)(141,374)(142,373)(143,372)(144,371)
(145,370)(146,369)(147,368)(148,367)(149,366)(150,365)(151,364)(152,363)
(153,343)(154,361)(155,360)(156,359)(157,358)(158,357)(159,356)(160,355)
(161,354)(162,353)(163,352)(164,351)(165,350)(166,349)(167,348)(168,347)
(169,346)(170,345)(171,344)(172,324)(173,342)(174,341)(175,340)(176,339)
(177,338)(178,337)(179,336)(180,335)(181,334)(182,333)(183,332)(184,331)
(185,330)(186,329)(187,328)(188,327)(189,326)(190,325);;
s2 := (  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)(  9, 13)
( 10, 12)( 20, 21)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)( 27, 33)
( 28, 32)( 29, 31)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)( 45, 53)
( 46, 52)( 47, 51)( 48, 50)( 58, 59)( 60, 76)( 61, 75)( 62, 74)( 63, 73)
( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 77, 78)( 79, 95)( 80, 94)( 81, 93)
( 82, 92)( 83, 91)( 84, 90)( 85, 89)( 86, 88)( 96, 97)( 98,114)( 99,113)
(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(115,116)(117,133)
(118,132)(119,131)(120,130)(121,129)(122,128)(123,127)(124,126)(134,135)
(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)(142,146)(143,145)
(153,154)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)
(162,164)(172,173)(174,190)(175,189)(176,188)(177,187)(178,186)(179,185)
(180,184)(181,183)(191,192)(193,209)(194,208)(195,207)(196,206)(197,205)
(198,204)(199,203)(200,202)(210,211)(212,228)(213,227)(214,226)(215,225)
(216,224)(217,223)(218,222)(219,221)(229,230)(231,247)(232,246)(233,245)
(234,244)(235,243)(236,242)(237,241)(238,240)(248,249)(250,266)(251,265)
(252,264)(253,263)(254,262)(255,261)(256,260)(257,259)(267,268)(269,285)
(270,284)(271,283)(272,282)(273,281)(274,280)(275,279)(276,278)(286,287)
(288,304)(289,303)(290,302)(291,301)(292,300)(293,299)(294,298)(295,297)
(305,306)(307,323)(308,322)(309,321)(310,320)(311,319)(312,318)(313,317)
(314,316)(324,325)(326,342)(327,341)(328,340)(329,339)(330,338)(331,337)
(332,336)(333,335)(343,344)(345,361)(346,360)(347,359)(348,358)(349,357)
(350,356)(351,355)(352,354)(362,363)(364,380)(365,379)(366,378)(367,377)
(368,376)(369,375)(370,374)(371,373);;
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*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*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(380)!( 20, 77)( 21, 78)( 22, 79)( 23, 80)( 24, 81)( 25, 82)( 26, 83)
( 27, 84)( 28, 85)( 29, 86)( 30, 87)( 31, 88)( 32, 89)( 33, 90)( 34, 91)
( 35, 92)( 36, 93)( 37, 94)( 38, 95)( 39, 58)( 40, 59)( 41, 60)( 42, 61)
( 43, 62)( 44, 63)( 45, 64)( 46, 65)( 47, 66)( 48, 67)( 49, 68)( 50, 69)
( 51, 70)( 52, 71)( 53, 72)( 54, 73)( 55, 74)( 56, 75)( 57, 76)(115,172)
(116,173)(117,174)(118,175)(119,176)(120,177)(121,178)(122,179)(123,180)
(124,181)(125,182)(126,183)(127,184)(128,185)(129,186)(130,187)(131,188)
(132,189)(133,190)(134,153)(135,154)(136,155)(137,156)(138,157)(139,158)
(140,159)(141,160)(142,161)(143,162)(144,163)(145,164)(146,165)(147,166)
(148,167)(149,168)(150,169)(151,170)(152,171)(191,286)(192,287)(193,288)
(194,289)(195,290)(196,291)(197,292)(198,293)(199,294)(200,295)(201,296)
(202,297)(203,298)(204,299)(205,300)(206,301)(207,302)(208,303)(209,304)
(210,362)(211,363)(212,364)(213,365)(214,366)(215,367)(216,368)(217,369)
(218,370)(219,371)(220,372)(221,373)(222,374)(223,375)(224,376)(225,377)
(226,378)(227,379)(228,380)(229,343)(230,344)(231,345)(232,346)(233,347)
(234,348)(235,349)(236,350)(237,351)(238,352)(239,353)(240,354)(241,355)
(242,356)(243,357)(244,358)(245,359)(246,360)(247,361)(248,324)(249,325)
(250,326)(251,327)(252,328)(253,329)(254,330)(255,331)(256,332)(257,333)
(258,334)(259,335)(260,336)(261,337)(262,338)(263,339)(264,340)(265,341)
(266,342)(267,305)(268,306)(269,307)(270,308)(271,309)(272,310)(273,311)
(274,312)(275,313)(276,314)(277,315)(278,316)(279,317)(280,318)(281,319)
(282,320)(283,321)(284,322)(285,323);
s1 := Sym(380)!(  1,210)(  2,228)(  3,227)(  4,226)(  5,225)(  6,224)(  7,223)
(  8,222)(  9,221)( 10,220)( 11,219)( 12,218)( 13,217)( 14,216)( 15,215)
( 16,214)( 17,213)( 18,212)( 19,211)( 20,191)( 21,209)( 22,208)( 23,207)
( 24,206)( 25,205)( 26,204)( 27,203)( 28,202)( 29,201)( 30,200)( 31,199)
( 32,198)( 33,197)( 34,196)( 35,195)( 36,194)( 37,193)( 38,192)( 39,267)
( 40,285)( 41,284)( 42,283)( 43,282)( 44,281)( 45,280)( 46,279)( 47,278)
( 48,277)( 49,276)( 50,275)( 51,274)( 52,273)( 53,272)( 54,271)( 55,270)
( 56,269)( 57,268)( 58,248)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)
( 64,261)( 65,260)( 66,259)( 67,258)( 68,257)( 69,256)( 70,255)( 71,254)
( 72,253)( 73,252)( 74,251)( 75,250)( 76,249)( 77,229)( 78,247)( 79,246)
( 80,245)( 81,244)( 82,243)( 83,242)( 84,241)( 85,240)( 86,239)( 87,238)
( 88,237)( 89,236)( 90,235)( 91,234)( 92,233)( 93,232)( 94,231)( 95,230)
( 96,305)( 97,323)( 98,322)( 99,321)(100,320)(101,319)(102,318)(103,317)
(104,316)(105,315)(106,314)(107,313)(108,312)(109,311)(110,310)(111,309)
(112,308)(113,307)(114,306)(115,286)(116,304)(117,303)(118,302)(119,301)
(120,300)(121,299)(122,298)(123,297)(124,296)(125,295)(126,294)(127,293)
(128,292)(129,291)(130,290)(131,289)(132,288)(133,287)(134,362)(135,380)
(136,379)(137,378)(138,377)(139,376)(140,375)(141,374)(142,373)(143,372)
(144,371)(145,370)(146,369)(147,368)(148,367)(149,366)(150,365)(151,364)
(152,363)(153,343)(154,361)(155,360)(156,359)(157,358)(158,357)(159,356)
(160,355)(161,354)(162,353)(163,352)(164,351)(165,350)(166,349)(167,348)
(168,347)(169,346)(170,345)(171,344)(172,324)(173,342)(174,341)(175,340)
(176,339)(177,338)(178,337)(179,336)(180,335)(181,334)(182,333)(183,332)
(184,331)(185,330)(186,329)(187,328)(188,327)(189,326)(190,325);
s2 := Sym(380)!(  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)
(  9, 13)( 10, 12)( 20, 21)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)
( 27, 33)( 28, 32)( 29, 31)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)
( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58, 59)( 60, 76)( 61, 75)( 62, 74)
( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 77, 78)( 79, 95)( 80, 94)
( 81, 93)( 82, 92)( 83, 91)( 84, 90)( 85, 89)( 86, 88)( 96, 97)( 98,114)
( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(115,116)
(117,133)(118,132)(119,131)(120,130)(121,129)(122,128)(123,127)(124,126)
(134,135)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)(142,146)
(143,145)(153,154)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)
(161,165)(162,164)(172,173)(174,190)(175,189)(176,188)(177,187)(178,186)
(179,185)(180,184)(181,183)(191,192)(193,209)(194,208)(195,207)(196,206)
(197,205)(198,204)(199,203)(200,202)(210,211)(212,228)(213,227)(214,226)
(215,225)(216,224)(217,223)(218,222)(219,221)(229,230)(231,247)(232,246)
(233,245)(234,244)(235,243)(236,242)(237,241)(238,240)(248,249)(250,266)
(251,265)(252,264)(253,263)(254,262)(255,261)(256,260)(257,259)(267,268)
(269,285)(270,284)(271,283)(272,282)(273,281)(274,280)(275,279)(276,278)
(286,287)(288,304)(289,303)(290,302)(291,301)(292,300)(293,299)(294,298)
(295,297)(305,306)(307,323)(308,322)(309,321)(310,320)(311,319)(312,318)
(313,317)(314,316)(324,325)(326,342)(327,341)(328,340)(329,339)(330,338)
(331,337)(332,336)(333,335)(343,344)(345,361)(346,360)(347,359)(348,358)
(349,357)(350,356)(351,355)(352,354)(362,363)(364,380)(365,379)(366,378)
(367,377)(368,376)(369,375)(370,374)(371,373);
poly := sub<Sym(380)|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*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*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