Polytope of Type {20,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,40}*1600b
if this polytope has a name.
Group : SmallGroup(1600,3130)
Rank : 3
Schlafli Type : {20,40}
Number of vertices, edges, etc : 20, 400, 40
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 10
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 : {20,20}*800c, {10,40}*800c
   4-fold quotients : {20,10}*400b, {10,20}*400c
   5-fold quotients : {20,8}*320a
   8-fold quotients : {10,10}*200c
   10-fold quotients : {20,4}*160, {10,8}*160
   16-fold quotients : {5,10}*100
   20-fold quotients : {20,2}*80, {10,4}*80
   25-fold quotients : {4,8}*64a
   40-fold quotients : {10,2}*40
   50-fold quotients : {4,4}*32, {2,8}*32
   80-fold quotients : {5,2}*20
   100-fold quotients : {2,4}*16, {4,2}*16
   200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)
( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)
( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)
( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)
(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)
(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)
(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)
(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)(161,166)
(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)(182,200)
(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)(190,192)
(201,376)(202,380)(203,379)(204,378)(205,377)(206,396)(207,400)(208,399)
(209,398)(210,397)(211,391)(212,395)(213,394)(214,393)(215,392)(216,386)
(217,390)(218,389)(219,388)(220,387)(221,381)(222,385)(223,384)(224,383)
(225,382)(226,351)(227,355)(228,354)(229,353)(230,352)(231,371)(232,375)
(233,374)(234,373)(235,372)(236,366)(237,370)(238,369)(239,368)(240,367)
(241,361)(242,365)(243,364)(244,363)(245,362)(246,356)(247,360)(248,359)
(249,358)(250,357)(251,301)(252,305)(253,304)(254,303)(255,302)(256,321)
(257,325)(258,324)(259,323)(260,322)(261,316)(262,320)(263,319)(264,318)
(265,317)(266,311)(267,315)(268,314)(269,313)(270,312)(271,306)(272,310)
(273,309)(274,308)(275,307)(276,326)(277,330)(278,329)(279,328)(280,327)
(281,346)(282,350)(283,349)(284,348)(285,347)(286,341)(287,345)(288,344)
(289,343)(290,342)(291,336)(292,340)(293,339)(294,338)(295,337)(296,331)
(297,335)(298,334)(299,333)(300,332);;
s1 := (  1,207)(  2,206)(  3,210)(  4,209)(  5,208)(  6,202)(  7,201)(  8,205)
(  9,204)( 10,203)( 11,222)( 12,221)( 13,225)( 14,224)( 15,223)( 16,217)
( 17,216)( 18,220)( 19,219)( 20,218)( 21,212)( 22,211)( 23,215)( 24,214)
( 25,213)( 26,232)( 27,231)( 28,235)( 29,234)( 30,233)( 31,227)( 32,226)
( 33,230)( 34,229)( 35,228)( 36,247)( 37,246)( 38,250)( 39,249)( 40,248)
( 41,242)( 42,241)( 43,245)( 44,244)( 45,243)( 46,237)( 47,236)( 48,240)
( 49,239)( 50,238)( 51,282)( 52,281)( 53,285)( 54,284)( 55,283)( 56,277)
( 57,276)( 58,280)( 59,279)( 60,278)( 61,297)( 62,296)( 63,300)( 64,299)
( 65,298)( 66,292)( 67,291)( 68,295)( 69,294)( 70,293)( 71,287)( 72,286)
( 73,290)( 74,289)( 75,288)( 76,257)( 77,256)( 78,260)( 79,259)( 80,258)
( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 86,272)( 87,271)( 88,275)
( 89,274)( 90,273)( 91,267)( 92,266)( 93,270)( 94,269)( 95,268)( 96,262)
( 97,261)( 98,265)( 99,264)(100,263)(101,332)(102,331)(103,335)(104,334)
(105,333)(106,327)(107,326)(108,330)(109,329)(110,328)(111,347)(112,346)
(113,350)(114,349)(115,348)(116,342)(117,341)(118,345)(119,344)(120,343)
(121,337)(122,336)(123,340)(124,339)(125,338)(126,307)(127,306)(128,310)
(129,309)(130,308)(131,302)(132,301)(133,305)(134,304)(135,303)(136,322)
(137,321)(138,325)(139,324)(140,323)(141,317)(142,316)(143,320)(144,319)
(145,318)(146,312)(147,311)(148,315)(149,314)(150,313)(151,357)(152,356)
(153,360)(154,359)(155,358)(156,352)(157,351)(158,355)(159,354)(160,353)
(161,372)(162,371)(163,375)(164,374)(165,373)(166,367)(167,366)(168,370)
(169,369)(170,368)(171,362)(172,361)(173,365)(174,364)(175,363)(176,382)
(177,381)(178,385)(179,384)(180,383)(181,377)(182,376)(183,380)(184,379)
(185,378)(186,397)(187,396)(188,400)(189,399)(190,398)(191,392)(192,391)
(193,395)(194,394)(195,393)(196,387)(197,386)(198,390)(199,389)(200,388);;
s2 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)( 54, 79)
( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)( 62, 92)
( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)
( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(101,126)(102,127)(103,128)
(104,129)(105,130)(106,146)(107,147)(108,148)(109,149)(110,150)(111,141)
(112,142)(113,143)(114,144)(115,145)(116,136)(117,137)(118,138)(119,139)
(120,140)(121,131)(122,132)(123,133)(124,134)(125,135)(156,171)(157,172)
(158,173)(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)
(181,196)(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)
(189,194)(190,195)(201,251)(202,252)(203,253)(204,254)(205,255)(206,271)
(207,272)(208,273)(209,274)(210,275)(211,266)(212,267)(213,268)(214,269)
(215,270)(216,261)(217,262)(218,263)(219,264)(220,265)(221,256)(222,257)
(223,258)(224,259)(225,260)(226,276)(227,277)(228,278)(229,279)(230,280)
(231,296)(232,297)(233,298)(234,299)(235,300)(236,291)(237,292)(238,293)
(239,294)(240,295)(241,286)(242,287)(243,288)(244,289)(245,290)(246,281)
(247,282)(248,283)(249,284)(250,285)(301,376)(302,377)(303,378)(304,379)
(305,380)(306,396)(307,397)(308,398)(309,399)(310,400)(311,391)(312,392)
(313,393)(314,394)(315,395)(316,386)(317,387)(318,388)(319,389)(320,390)
(321,381)(322,382)(323,383)(324,384)(325,385)(326,351)(327,352)(328,353)
(329,354)(330,355)(331,371)(332,372)(333,373)(334,374)(335,375)(336,366)
(337,367)(338,368)(339,369)(340,370)(341,361)(342,362)(343,363)(344,364)
(345,365)(346,356)(347,357)(348,358)(349,359)(350,360);;
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*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*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, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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(400)!(  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)
( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)
( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)
( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)
( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)
( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)
(111,116)(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)
(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)
(140,142)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)
(161,166)(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)
(182,200)(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)
(190,192)(201,376)(202,380)(203,379)(204,378)(205,377)(206,396)(207,400)
(208,399)(209,398)(210,397)(211,391)(212,395)(213,394)(214,393)(215,392)
(216,386)(217,390)(218,389)(219,388)(220,387)(221,381)(222,385)(223,384)
(224,383)(225,382)(226,351)(227,355)(228,354)(229,353)(230,352)(231,371)
(232,375)(233,374)(234,373)(235,372)(236,366)(237,370)(238,369)(239,368)
(240,367)(241,361)(242,365)(243,364)(244,363)(245,362)(246,356)(247,360)
(248,359)(249,358)(250,357)(251,301)(252,305)(253,304)(254,303)(255,302)
(256,321)(257,325)(258,324)(259,323)(260,322)(261,316)(262,320)(263,319)
(264,318)(265,317)(266,311)(267,315)(268,314)(269,313)(270,312)(271,306)
(272,310)(273,309)(274,308)(275,307)(276,326)(277,330)(278,329)(279,328)
(280,327)(281,346)(282,350)(283,349)(284,348)(285,347)(286,341)(287,345)
(288,344)(289,343)(290,342)(291,336)(292,340)(293,339)(294,338)(295,337)
(296,331)(297,335)(298,334)(299,333)(300,332);
s1 := Sym(400)!(  1,207)(  2,206)(  3,210)(  4,209)(  5,208)(  6,202)(  7,201)
(  8,205)(  9,204)( 10,203)( 11,222)( 12,221)( 13,225)( 14,224)( 15,223)
( 16,217)( 17,216)( 18,220)( 19,219)( 20,218)( 21,212)( 22,211)( 23,215)
( 24,214)( 25,213)( 26,232)( 27,231)( 28,235)( 29,234)( 30,233)( 31,227)
( 32,226)( 33,230)( 34,229)( 35,228)( 36,247)( 37,246)( 38,250)( 39,249)
( 40,248)( 41,242)( 42,241)( 43,245)( 44,244)( 45,243)( 46,237)( 47,236)
( 48,240)( 49,239)( 50,238)( 51,282)( 52,281)( 53,285)( 54,284)( 55,283)
( 56,277)( 57,276)( 58,280)( 59,279)( 60,278)( 61,297)( 62,296)( 63,300)
( 64,299)( 65,298)( 66,292)( 67,291)( 68,295)( 69,294)( 70,293)( 71,287)
( 72,286)( 73,290)( 74,289)( 75,288)( 76,257)( 77,256)( 78,260)( 79,259)
( 80,258)( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 86,272)( 87,271)
( 88,275)( 89,274)( 90,273)( 91,267)( 92,266)( 93,270)( 94,269)( 95,268)
( 96,262)( 97,261)( 98,265)( 99,264)(100,263)(101,332)(102,331)(103,335)
(104,334)(105,333)(106,327)(107,326)(108,330)(109,329)(110,328)(111,347)
(112,346)(113,350)(114,349)(115,348)(116,342)(117,341)(118,345)(119,344)
(120,343)(121,337)(122,336)(123,340)(124,339)(125,338)(126,307)(127,306)
(128,310)(129,309)(130,308)(131,302)(132,301)(133,305)(134,304)(135,303)
(136,322)(137,321)(138,325)(139,324)(140,323)(141,317)(142,316)(143,320)
(144,319)(145,318)(146,312)(147,311)(148,315)(149,314)(150,313)(151,357)
(152,356)(153,360)(154,359)(155,358)(156,352)(157,351)(158,355)(159,354)
(160,353)(161,372)(162,371)(163,375)(164,374)(165,373)(166,367)(167,366)
(168,370)(169,369)(170,368)(171,362)(172,361)(173,365)(174,364)(175,363)
(176,382)(177,381)(178,385)(179,384)(180,383)(181,377)(182,376)(183,380)
(184,379)(185,378)(186,397)(187,396)(188,400)(189,399)(190,398)(191,392)
(192,391)(193,395)(194,394)(195,393)(196,387)(197,386)(198,390)(199,389)
(200,388);
s2 := Sym(400)!(  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)
( 54, 79)( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)
( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)
( 70, 90)( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(101,126)(102,127)
(103,128)(104,129)(105,130)(106,146)(107,147)(108,148)(109,149)(110,150)
(111,141)(112,142)(113,143)(114,144)(115,145)(116,136)(117,137)(118,138)
(119,139)(120,140)(121,131)(122,132)(123,133)(124,134)(125,135)(156,171)
(157,172)(158,173)(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)
(165,170)(181,196)(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)
(188,193)(189,194)(190,195)(201,251)(202,252)(203,253)(204,254)(205,255)
(206,271)(207,272)(208,273)(209,274)(210,275)(211,266)(212,267)(213,268)
(214,269)(215,270)(216,261)(217,262)(218,263)(219,264)(220,265)(221,256)
(222,257)(223,258)(224,259)(225,260)(226,276)(227,277)(228,278)(229,279)
(230,280)(231,296)(232,297)(233,298)(234,299)(235,300)(236,291)(237,292)
(238,293)(239,294)(240,295)(241,286)(242,287)(243,288)(244,289)(245,290)
(246,281)(247,282)(248,283)(249,284)(250,285)(301,376)(302,377)(303,378)
(304,379)(305,380)(306,396)(307,397)(308,398)(309,399)(310,400)(311,391)
(312,392)(313,393)(314,394)(315,395)(316,386)(317,387)(318,388)(319,389)
(320,390)(321,381)(322,382)(323,383)(324,384)(325,385)(326,351)(327,352)
(328,353)(329,354)(330,355)(331,371)(332,372)(333,373)(334,374)(335,375)
(336,366)(337,367)(338,368)(339,369)(340,370)(341,361)(342,362)(343,363)
(344,364)(345,365)(346,356)(347,357)(348,358)(349,359)(350,360);
poly := sub<Sym(400)|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*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*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, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope