Polytope of Type {40,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,20}*1600a
if this polytope has a name.
Group : SmallGroup(1600,2931)
Rank : 3
Schlafli Type : {40,20}
Number of vertices, edges, etc : 40, 400, 20
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 20
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) :
   2-fold quotients : {20,20}*800b
   4-fold quotients : {10,20}*400b, {20,10}*400c
   5-fold quotients : {8,20}*320b
   8-fold quotients : {10,10}*200b
   10-fold quotients : {4,20}*160
   16-fold quotients : {10,5}*100
   20-fold quotients : {2,20}*80, {4,10}*80
   25-fold quotients : {8,4}*64b
   40-fold quotients : {2,10}*40
   50-fold quotients : {4,4}*32
   80-fold quotients : {2,5}*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 := (  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);;
s1 := (  1,206)(  2,210)(  3,209)(  4,208)(  5,207)(  6,201)(  7,205)(  8,204)
(  9,203)( 10,202)( 11,221)( 12,225)( 13,224)( 14,223)( 15,222)( 16,216)
( 17,220)( 18,219)( 19,218)( 20,217)( 21,211)( 22,215)( 23,214)( 24,213)
( 25,212)( 26,231)( 27,235)( 28,234)( 29,233)( 30,232)( 31,226)( 32,230)
( 33,229)( 34,228)( 35,227)( 36,246)( 37,250)( 38,249)( 39,248)( 40,247)
( 41,241)( 42,245)( 43,244)( 44,243)( 45,242)( 46,236)( 47,240)( 48,239)
( 49,238)( 50,237)( 51,281)( 52,285)( 53,284)( 54,283)( 55,282)( 56,276)
( 57,280)( 58,279)( 59,278)( 60,277)( 61,296)( 62,300)( 63,299)( 64,298)
( 65,297)( 66,291)( 67,295)( 68,294)( 69,293)( 70,292)( 71,286)( 72,290)
( 73,289)( 74,288)( 75,287)( 76,256)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,271)( 87,275)( 88,274)
( 89,273)( 90,272)( 91,266)( 92,270)( 93,269)( 94,268)( 95,267)( 96,261)
( 97,265)( 98,264)( 99,263)(100,262)(101,331)(102,335)(103,334)(104,333)
(105,332)(106,326)(107,330)(108,329)(109,328)(110,327)(111,346)(112,350)
(113,349)(114,348)(115,347)(116,341)(117,345)(118,344)(119,343)(120,342)
(121,336)(122,340)(123,339)(124,338)(125,337)(126,306)(127,310)(128,309)
(129,308)(130,307)(131,301)(132,305)(133,304)(134,303)(135,302)(136,321)
(137,325)(138,324)(139,323)(140,322)(141,316)(142,320)(143,319)(144,318)
(145,317)(146,311)(147,315)(148,314)(149,313)(150,312)(151,356)(152,360)
(153,359)(154,358)(155,357)(156,351)(157,355)(158,354)(159,353)(160,352)
(161,371)(162,375)(163,374)(164,373)(165,372)(166,366)(167,370)(168,369)
(169,368)(170,367)(171,361)(172,365)(173,364)(174,363)(175,362)(176,381)
(177,385)(178,384)(179,383)(180,382)(181,376)(182,380)(183,379)(184,378)
(185,377)(186,396)(187,400)(188,399)(189,398)(190,397)(191,391)(192,395)
(193,394)(194,393)(195,392)(196,386)(197,390)(198,389)(199,388)(200,387);;
s2 := (  1,  2)(  3,  5)(  6, 22)(  7, 21)(  8, 25)(  9, 24)( 10, 23)( 11, 17)
( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 27)( 28, 30)( 31, 47)( 32, 46)
( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)
( 51, 77)( 52, 76)( 53, 80)( 54, 79)( 55, 78)( 56, 97)( 57, 96)( 58,100)
( 59, 99)( 60, 98)( 61, 92)( 62, 91)( 63, 95)( 64, 94)( 65, 93)( 66, 87)
( 67, 86)( 68, 90)( 69, 89)( 70, 88)( 71, 82)( 72, 81)( 73, 85)( 74, 84)
( 75, 83)(101,127)(102,126)(103,130)(104,129)(105,128)(106,147)(107,146)
(108,150)(109,149)(110,148)(111,142)(112,141)(113,145)(114,144)(115,143)
(116,137)(117,136)(118,140)(119,139)(120,138)(121,132)(122,131)(123,135)
(124,134)(125,133)(151,152)(153,155)(156,172)(157,171)(158,175)(159,174)
(160,173)(161,167)(162,166)(163,170)(164,169)(165,168)(176,177)(178,180)
(181,197)(182,196)(183,200)(184,199)(185,198)(186,192)(187,191)(188,195)
(189,194)(190,193)(201,352)(202,351)(203,355)(204,354)(205,353)(206,372)
(207,371)(208,375)(209,374)(210,373)(211,367)(212,366)(213,370)(214,369)
(215,368)(216,362)(217,361)(218,365)(219,364)(220,363)(221,357)(222,356)
(223,360)(224,359)(225,358)(226,377)(227,376)(228,380)(229,379)(230,378)
(231,397)(232,396)(233,400)(234,399)(235,398)(236,392)(237,391)(238,395)
(239,394)(240,393)(241,387)(242,386)(243,390)(244,389)(245,388)(246,382)
(247,381)(248,385)(249,384)(250,383)(251,302)(252,301)(253,305)(254,304)
(255,303)(256,322)(257,321)(258,325)(259,324)(260,323)(261,317)(262,316)
(263,320)(264,319)(265,318)(266,312)(267,311)(268,315)(269,314)(270,313)
(271,307)(272,306)(273,310)(274,309)(275,308)(276,327)(277,326)(278,330)
(279,329)(280,328)(281,347)(282,346)(283,350)(284,349)(285,348)(286,342)
(287,341)(288,345)(289,344)(290,343)(291,337)(292,336)(293,340)(294,339)
(295,338)(296,332)(297,331)(298,335)(299,334)(300,333);;
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*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope