Polytope of Type {2,4,25}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,25}*1600
if this polytope has a name.
Group : SmallGroup(1600,5601)
Rank : 4
Schlafli Type : {2,4,25}
Number of vertices, edges, etc : 2, 16, 200, 100
Order of s₀s₁s₂s₃ : 50
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   5-fold quotients : {2,4,5}*320
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)(  9, 17)( 10, 18)
( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)
( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)
( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)( 58, 66)
( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)( 74, 82)
( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)
( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)
(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(121,129)(122,130)
(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146)
(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(153,161)(154,162)
(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(169,177)(170,178)
(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)(186,194)
(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)(201,209)(202,210)
(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)(217,225)(218,226)
(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)(233,241)(234,242)
(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)(249,257)(250,258)
(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(265,273)(266,274)
(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(281,289)(282,290)
(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)(297,305)(298,306)
(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)(313,321)(314,322)
(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)(329,337)(330,338)
(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)(345,353)(346,354)
(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)(361,369)(362,370)
(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)(377,385)(378,386)
(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)(393,401)(394,402);;
s2 := (  4, 11)(  5, 18)(  6, 10)(  8, 15)(  9, 14)( 13, 17)( 19, 67)( 20, 75)
( 21, 82)( 22, 74)( 23, 71)( 24, 79)( 25, 78)( 26, 70)( 27, 68)( 28, 76)
( 29, 81)( 30, 73)( 31, 72)( 32, 80)( 33, 77)( 34, 69)( 35, 51)( 36, 59)
( 37, 66)( 38, 58)( 39, 55)( 40, 63)( 41, 62)( 42, 54)( 43, 52)( 44, 60)
( 45, 65)( 46, 57)( 47, 56)( 48, 64)( 49, 61)( 50, 53)( 83,339)( 84,347)
( 85,354)( 86,346)( 87,343)( 88,351)( 89,350)( 90,342)( 91,340)( 92,348)
( 93,353)( 94,345)( 95,344)( 96,352)( 97,349)( 98,341)( 99,323)(100,331)
(101,338)(102,330)(103,327)(104,335)(105,334)(106,326)(107,324)(108,332)
(109,337)(110,329)(111,328)(112,336)(113,333)(114,325)(115,387)(116,395)
(117,402)(118,394)(119,391)(120,399)(121,398)(122,390)(123,388)(124,396)
(125,401)(126,393)(127,392)(128,400)(129,397)(130,389)(131,371)(132,379)
(133,386)(134,378)(135,375)(136,383)(137,382)(138,374)(139,372)(140,380)
(141,385)(142,377)(143,376)(144,384)(145,381)(146,373)(147,355)(148,363)
(149,370)(150,362)(151,359)(152,367)(153,366)(154,358)(155,356)(156,364)
(157,369)(158,361)(159,360)(160,368)(161,365)(162,357)(163,259)(164,267)
(165,274)(166,266)(167,263)(168,271)(169,270)(170,262)(171,260)(172,268)
(173,273)(174,265)(175,264)(176,272)(177,269)(178,261)(179,243)(180,251)
(181,258)(182,250)(183,247)(184,255)(185,254)(186,246)(187,244)(188,252)
(189,257)(190,249)(191,248)(192,256)(193,253)(194,245)(195,307)(196,315)
(197,322)(198,314)(199,311)(200,319)(201,318)(202,310)(203,308)(204,316)
(205,321)(206,313)(207,312)(208,320)(209,317)(210,309)(211,291)(212,299)
(213,306)(214,298)(215,295)(216,303)(217,302)(218,294)(219,292)(220,300)
(221,305)(222,297)(223,296)(224,304)(225,301)(226,293)(227,275)(228,283)
(229,290)(230,282)(231,279)(232,287)(233,286)(234,278)(235,276)(236,284)
(237,289)(238,281)(239,280)(240,288)(241,285)(242,277);;
s3 := (  3, 83)(  4, 93)(  5, 92)(  6, 86)(  7, 95)(  8, 89)(  9, 88)( 10, 98)
( 11, 91)( 12, 85)( 13, 84)( 14, 94)( 15, 87)( 16, 97)( 17, 96)( 18, 90)
( 19,147)( 20,157)( 21,156)( 22,150)( 23,159)( 24,153)( 25,152)( 26,162)
( 27,155)( 28,149)( 29,148)( 30,158)( 31,151)( 32,161)( 33,160)( 34,154)
( 35,131)( 36,141)( 37,140)( 38,134)( 39,143)( 40,137)( 41,136)( 42,146)
( 43,139)( 44,133)( 45,132)( 46,142)( 47,135)( 48,145)( 49,144)( 50,138)
( 51,115)( 52,125)( 53,124)( 54,118)( 55,127)( 56,121)( 57,120)( 58,130)
( 59,123)( 60,117)( 61,116)( 62,126)( 63,119)( 64,129)( 65,128)( 66,122)
( 67, 99)( 68,109)( 69,108)( 70,102)( 71,111)( 72,105)( 73,104)( 74,114)
( 75,107)( 76,101)( 77,100)( 78,110)( 79,103)( 80,113)( 81,112)( 82,106)
(163,339)(164,349)(165,348)(166,342)(167,351)(168,345)(169,344)(170,354)
(171,347)(172,341)(173,340)(174,350)(175,343)(176,353)(177,352)(178,346)
(179,323)(180,333)(181,332)(182,326)(183,335)(184,329)(185,328)(186,338)
(187,331)(188,325)(189,324)(190,334)(191,327)(192,337)(193,336)(194,330)
(195,387)(196,397)(197,396)(198,390)(199,399)(200,393)(201,392)(202,402)
(203,395)(204,389)(205,388)(206,398)(207,391)(208,401)(209,400)(210,394)
(211,371)(212,381)(213,380)(214,374)(215,383)(216,377)(217,376)(218,386)
(219,379)(220,373)(221,372)(222,382)(223,375)(224,385)(225,384)(226,378)
(227,355)(228,365)(229,364)(230,358)(231,367)(232,361)(233,360)(234,370)
(235,363)(236,357)(237,356)(238,366)(239,359)(240,369)(241,368)(242,362)
(243,259)(244,269)(245,268)(246,262)(247,271)(248,265)(249,264)(250,274)
(251,267)(252,261)(253,260)(254,270)(255,263)(256,273)(257,272)(258,266)
(275,307)(276,317)(277,316)(278,310)(279,319)(280,313)(281,312)(282,322)
(283,315)(284,309)(285,308)(286,318)(287,311)(288,321)(289,320)(290,314)
(292,301)(293,300)(295,303)(296,297)(298,306)(304,305);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(402)!(1,2);
s1 := Sym(402)!(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)(  9, 17)
( 10, 18)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)
( 26, 34)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)
( 42, 50)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)
( 58, 66)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)
( 74, 82)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)
( 90, 98)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)
(106,114)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(121,129)
(122,130)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)
(138,146)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(153,161)
(154,162)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(169,177)
(170,178)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)
(186,194)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)(201,209)
(202,210)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)(217,225)
(218,226)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)(233,241)
(234,242)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)(249,257)
(250,258)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(265,273)
(266,274)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(281,289)
(282,290)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)(297,305)
(298,306)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)(313,321)
(314,322)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)(329,337)
(330,338)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)(345,353)
(346,354)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)(361,369)
(362,370)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)(377,385)
(378,386)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)(393,401)
(394,402);
s2 := Sym(402)!(  4, 11)(  5, 18)(  6, 10)(  8, 15)(  9, 14)( 13, 17)( 19, 67)
( 20, 75)( 21, 82)( 22, 74)( 23, 71)( 24, 79)( 25, 78)( 26, 70)( 27, 68)
( 28, 76)( 29, 81)( 30, 73)( 31, 72)( 32, 80)( 33, 77)( 34, 69)( 35, 51)
( 36, 59)( 37, 66)( 38, 58)( 39, 55)( 40, 63)( 41, 62)( 42, 54)( 43, 52)
( 44, 60)( 45, 65)( 46, 57)( 47, 56)( 48, 64)( 49, 61)( 50, 53)( 83,339)
( 84,347)( 85,354)( 86,346)( 87,343)( 88,351)( 89,350)( 90,342)( 91,340)
( 92,348)( 93,353)( 94,345)( 95,344)( 96,352)( 97,349)( 98,341)( 99,323)
(100,331)(101,338)(102,330)(103,327)(104,335)(105,334)(106,326)(107,324)
(108,332)(109,337)(110,329)(111,328)(112,336)(113,333)(114,325)(115,387)
(116,395)(117,402)(118,394)(119,391)(120,399)(121,398)(122,390)(123,388)
(124,396)(125,401)(126,393)(127,392)(128,400)(129,397)(130,389)(131,371)
(132,379)(133,386)(134,378)(135,375)(136,383)(137,382)(138,374)(139,372)
(140,380)(141,385)(142,377)(143,376)(144,384)(145,381)(146,373)(147,355)
(148,363)(149,370)(150,362)(151,359)(152,367)(153,366)(154,358)(155,356)
(156,364)(157,369)(158,361)(159,360)(160,368)(161,365)(162,357)(163,259)
(164,267)(165,274)(166,266)(167,263)(168,271)(169,270)(170,262)(171,260)
(172,268)(173,273)(174,265)(175,264)(176,272)(177,269)(178,261)(179,243)
(180,251)(181,258)(182,250)(183,247)(184,255)(185,254)(186,246)(187,244)
(188,252)(189,257)(190,249)(191,248)(192,256)(193,253)(194,245)(195,307)
(196,315)(197,322)(198,314)(199,311)(200,319)(201,318)(202,310)(203,308)
(204,316)(205,321)(206,313)(207,312)(208,320)(209,317)(210,309)(211,291)
(212,299)(213,306)(214,298)(215,295)(216,303)(217,302)(218,294)(219,292)
(220,300)(221,305)(222,297)(223,296)(224,304)(225,301)(226,293)(227,275)
(228,283)(229,290)(230,282)(231,279)(232,287)(233,286)(234,278)(235,276)
(236,284)(237,289)(238,281)(239,280)(240,288)(241,285)(242,277);
s3 := Sym(402)!(  3, 83)(  4, 93)(  5, 92)(  6, 86)(  7, 95)(  8, 89)(  9, 88)
( 10, 98)( 11, 91)( 12, 85)( 13, 84)( 14, 94)( 15, 87)( 16, 97)( 17, 96)
( 18, 90)( 19,147)( 20,157)( 21,156)( 22,150)( 23,159)( 24,153)( 25,152)
( 26,162)( 27,155)( 28,149)( 29,148)( 30,158)( 31,151)( 32,161)( 33,160)
( 34,154)( 35,131)( 36,141)( 37,140)( 38,134)( 39,143)( 40,137)( 41,136)
( 42,146)( 43,139)( 44,133)( 45,132)( 46,142)( 47,135)( 48,145)( 49,144)
( 50,138)( 51,115)( 52,125)( 53,124)( 54,118)( 55,127)( 56,121)( 57,120)
( 58,130)( 59,123)( 60,117)( 61,116)( 62,126)( 63,119)( 64,129)( 65,128)
( 66,122)( 67, 99)( 68,109)( 69,108)( 70,102)( 71,111)( 72,105)( 73,104)
( 74,114)( 75,107)( 76,101)( 77,100)( 78,110)( 79,103)( 80,113)( 81,112)
( 82,106)(163,339)(164,349)(165,348)(166,342)(167,351)(168,345)(169,344)
(170,354)(171,347)(172,341)(173,340)(174,350)(175,343)(176,353)(177,352)
(178,346)(179,323)(180,333)(181,332)(182,326)(183,335)(184,329)(185,328)
(186,338)(187,331)(188,325)(189,324)(190,334)(191,327)(192,337)(193,336)
(194,330)(195,387)(196,397)(197,396)(198,390)(199,399)(200,393)(201,392)
(202,402)(203,395)(204,389)(205,388)(206,398)(207,391)(208,401)(209,400)
(210,394)(211,371)(212,381)(213,380)(214,374)(215,383)(216,377)(217,376)
(218,386)(219,379)(220,373)(221,372)(222,382)(223,375)(224,385)(225,384)
(226,378)(227,355)(228,365)(229,364)(230,358)(231,367)(232,361)(233,360)
(234,370)(235,363)(236,357)(237,356)(238,366)(239,359)(240,369)(241,368)
(242,362)(243,259)(244,269)(245,268)(246,262)(247,271)(248,265)(249,264)
(250,274)(251,267)(252,261)(253,260)(254,270)(255,263)(256,273)(257,272)
(258,266)(275,307)(276,317)(277,316)(278,310)(279,319)(280,313)(281,312)
(282,322)(283,315)(284,309)(285,308)(286,318)(287,311)(288,321)(289,320)
(290,314)(292,301)(293,300)(295,303)(296,297)(298,306)(304,305);
poly := sub<Sym(402)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope