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Polytope of Type {20,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,40}*1600a
if this polytope has a name.
Group : SmallGroup(1600,2931)
Rank : 3
Schlafli Type : {20,40}
Number of vertices, edges, etc : 20, 400, 40
Order of s0s1s2 : 40
Order of s0s1s2s1 : 20
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
   4-fold quotients : {20,10}*400b, {10,20}*400c
   5-fold quotients : {20,8}*320b
   8-fold quotients : {10,10}*200c
   10-fold quotients : {20,4}*160
   16-fold quotients : {5,10}*100
   20-fold quotients : {20,2}*80, {10,4}*80
   25-fold quotients : {4,8}*64b
   40-fold quotients : {10,2}*40
   50-fold quotients : {4,4}*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)
( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56, 96)( 57,100)( 58, 99)
( 59, 98)( 60, 97)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)( 66, 86)
( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 81)( 72, 85)( 73, 84)( 74, 83)
( 75, 82)(101,126)(102,130)(103,129)(104,128)(105,127)(106,146)(107,150)
(108,149)(109,148)(110,147)(111,141)(112,145)(113,144)(114,143)(115,142)
(116,136)(117,140)(118,139)(119,138)(120,137)(121,131)(122,135)(123,134)
(124,133)(125,132)(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)(201,351)(202,355)(203,354)(204,353)(205,352)(206,371)
(207,375)(208,374)(209,373)(210,372)(211,366)(212,370)(213,369)(214,368)
(215,367)(216,361)(217,365)(218,364)(219,363)(220,362)(221,356)(222,360)
(223,359)(224,358)(225,357)(226,376)(227,380)(228,379)(229,378)(230,377)
(231,396)(232,400)(233,399)(234,398)(235,397)(236,391)(237,395)(238,394)
(239,393)(240,392)(241,386)(242,390)(243,389)(244,388)(245,387)(246,381)
(247,385)(248,384)(249,383)(250,382)(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)(106,121)(107,122)(108,123)
(109,124)(110,125)(111,116)(112,117)(113,118)(114,119)(115,120)(131,146)
(132,147)(133,148)(134,149)(135,150)(136,141)(137,142)(138,143)(139,144)
(140,145)(151,176)(152,177)(153,178)(154,179)(155,180)(156,196)(157,197)
(158,198)(159,199)(160,200)(161,191)(162,192)(163,193)(164,194)(165,195)
(166,186)(167,187)(168,188)(169,189)(170,190)(171,181)(172,182)(173,183)
(174,184)(175,185)(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)(301,351)(302,352)(303,353)(304,354)
(305,355)(306,371)(307,372)(308,373)(309,374)(310,375)(311,366)(312,367)
(313,368)(314,369)(315,370)(316,361)(317,362)(318,363)(319,364)(320,365)
(321,356)(322,357)(323,358)(324,359)(325,360)(326,376)(327,377)(328,378)
(329,379)(330,380)(331,396)(332,397)(333,398)(334,399)(335,400)(336,391)
(337,392)(338,393)(339,394)(340,395)(341,386)(342,387)(343,388)(344,389)
(345,390)(346,381)(347,382)(348,383)(349,384)(350,385);;
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*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)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56, 96)( 57,100)
( 58, 99)( 59, 98)( 60, 97)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)
( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 81)( 72, 85)( 73, 84)
( 74, 83)( 75, 82)(101,126)(102,130)(103,129)(104,128)(105,127)(106,146)
(107,150)(108,149)(109,148)(110,147)(111,141)(112,145)(113,144)(114,143)
(115,142)(116,136)(117,140)(118,139)(119,138)(120,137)(121,131)(122,135)
(123,134)(124,133)(125,132)(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)(201,351)(202,355)(203,354)(204,353)(205,352)
(206,371)(207,375)(208,374)(209,373)(210,372)(211,366)(212,370)(213,369)
(214,368)(215,367)(216,361)(217,365)(218,364)(219,363)(220,362)(221,356)
(222,360)(223,359)(224,358)(225,357)(226,376)(227,380)(228,379)(229,378)
(230,377)(231,396)(232,400)(233,399)(234,398)(235,397)(236,391)(237,395)
(238,394)(239,393)(240,392)(241,386)(242,390)(243,389)(244,388)(245,387)
(246,381)(247,385)(248,384)(249,383)(250,382)(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)(106,121)(107,122)
(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)(114,119)(115,120)
(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)(137,142)(138,143)
(139,144)(140,145)(151,176)(152,177)(153,178)(154,179)(155,180)(156,196)
(157,197)(158,198)(159,199)(160,200)(161,191)(162,192)(163,193)(164,194)
(165,195)(166,186)(167,187)(168,188)(169,189)(170,190)(171,181)(172,182)
(173,183)(174,184)(175,185)(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)(301,351)(302,352)(303,353)
(304,354)(305,355)(306,371)(307,372)(308,373)(309,374)(310,375)(311,366)
(312,367)(313,368)(314,369)(315,370)(316,361)(317,362)(318,363)(319,364)
(320,365)(321,356)(322,357)(323,358)(324,359)(325,360)(326,376)(327,377)
(328,378)(329,379)(330,380)(331,396)(332,397)(333,398)(334,399)(335,400)
(336,391)(337,392)(338,393)(339,394)(340,395)(341,386)(342,387)(343,388)
(344,389)(345,390)(346,381)(347,382)(348,383)(349,384)(350,385);
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*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*s0*s1 >; 
 
References : None.
to this polytope