Polytope of Type {16,50}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,50}*1600
Also Known As : {16,50|2}. if this polytope has another name.
Group : SmallGroup(1600,537)
Rank : 3
Schlafli Type : {16,50}
Number of vertices, edges, etc : 16, 400, 50
Order of s₀s₁s₂ : 400
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 : {8,50}*800
   4-fold quotients : {4,50}*400
   5-fold quotients : {16,10}*320
   8-fold quotients : {2,50}*200
   10-fold quotients : {8,10}*160
   16-fold quotients : {2,25}*100
   20-fold quotients : {4,10}*80
   25-fold quotients : {16,2}*64
   40-fold quotients : {2,10}*40
   50-fold quotients : {8,2}*32
   80-fold quotients : {2,5}*20
   100-fold quotients : {4,2}*16
   200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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