Polytope of Type {40,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,20}*1600b
if this polytope has a name.
Group : SmallGroup(1600,3130)
Rank : 3
Schlafli Type : {40,20}
Number of vertices, edges, etc : 40, 400, 20
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 10
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, {40,10}*800c
   4-fold quotients : {10,20}*400b, {20,10}*400c
   5-fold quotients : {8,20}*320a
   8-fold quotients : {10,10}*200b
   10-fold quotients : {4,20}*160, {8,10}*160
   16-fold quotients : {10,5}*100
   20-fold quotients : {2,20}*80, {4,10}*80
   25-fold quotients : {8,4}*64a
   40-fold quotients : {2,10}*40
   50-fold quotients : {4,4}*32, {8,2}*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)(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);;
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, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)( 61, 67)
( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76, 77)( 78, 80)( 81, 97)( 82, 96)
( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)( 90, 93)
(101,102)(103,105)(106,122)(107,121)(108,125)(109,124)(110,123)(111,117)
(112,116)(113,120)(114,119)(115,118)(126,127)(128,130)(131,147)(132,146)
(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)(139,144)(140,143)
(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)
(201,377)(202,376)(203,380)(204,379)(205,378)(206,397)(207,396)(208,400)
(209,399)(210,398)(211,392)(212,391)(213,395)(214,394)(215,393)(216,387)
(217,386)(218,390)(219,389)(220,388)(221,382)(222,381)(223,385)(224,384)
(225,383)(226,352)(227,351)(228,355)(229,354)(230,353)(231,372)(232,371)
(233,375)(234,374)(235,373)(236,367)(237,366)(238,370)(239,369)(240,368)
(241,362)(242,361)(243,365)(244,364)(245,363)(246,357)(247,356)(248,360)
(249,359)(250,358)(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*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*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*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 ];;
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)(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);
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, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)
( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76, 77)( 78, 80)( 81, 97)
( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)
( 90, 93)(101,102)(103,105)(106,122)(107,121)(108,125)(109,124)(110,123)
(111,117)(112,116)(113,120)(114,119)(115,118)(126,127)(128,130)(131,147)
(132,146)(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)(139,144)
(140,143)(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)(201,377)(202,376)(203,380)(204,379)(205,378)(206,397)(207,396)
(208,400)(209,399)(210,398)(211,392)(212,391)(213,395)(214,394)(215,393)
(216,387)(217,386)(218,390)(219,389)(220,388)(221,382)(222,381)(223,385)
(224,384)(225,383)(226,352)(227,351)(228,355)(229,354)(230,353)(231,372)
(232,371)(233,375)(234,374)(235,373)(236,367)(237,366)(238,370)(239,369)
(240,368)(241,362)(242,361)(243,365)(244,364)(245,363)(246,357)(247,356)
(248,360)(249,359)(250,358)(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*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*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*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 >;

References : None.
to this polytope