Polytope of Type {2,25,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,25,4}*1600
if this polytope has a name.
Group : SmallGroup(1600,5601)
Rank : 4
Schlafli Type : {2,25,4}
Number of vertices, edges, etc : 2, 100, 200, 16
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 : {2,5,4}*320
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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);;
s2 := ( 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);;
s3 := ( 3, 7)( 4, 8)( 5, 9)( 6, 10)( 11, 15)( 12, 16)( 13, 17)( 14, 18)
( 19, 23)( 20, 24)( 21, 25)( 22, 26)( 27, 31)( 28, 32)( 29, 33)( 30, 34)
( 35, 39)( 36, 40)( 37, 41)( 38, 42)( 43, 47)( 44, 48)( 45, 49)( 46, 50)
( 51, 55)( 52, 56)( 53, 57)( 54, 58)( 59, 63)( 60, 64)( 61, 65)( 62, 66)
( 67, 71)( 68, 72)( 69, 73)( 70, 74)( 75, 79)( 76, 80)( 77, 81)( 78, 82)
( 83, 87)( 84, 88)( 85, 89)( 86, 90)( 91, 95)( 92, 96)( 93, 97)( 94, 98)
( 99,103)(100,104)(101,105)(102,106)(107,111)(108,112)(109,113)(110,114)
(115,119)(116,120)(117,121)(118,122)(123,127)(124,128)(125,129)(126,130)
(131,135)(132,136)(133,137)(134,138)(139,143)(140,144)(141,145)(142,146)
(147,151)(148,152)(149,153)(150,154)(155,159)(156,160)(157,161)(158,162)
(163,167)(164,168)(165,169)(166,170)(171,175)(172,176)(173,177)(174,178)
(179,183)(180,184)(181,185)(182,186)(187,191)(188,192)(189,193)(190,194)
(195,199)(196,200)(197,201)(198,202)(203,207)(204,208)(205,209)(206,210)
(211,215)(212,216)(213,217)(214,218)(219,223)(220,224)(221,225)(222,226)
(227,231)(228,232)(229,233)(230,234)(235,239)(236,240)(237,241)(238,242)
(243,247)(244,248)(245,249)(246,250)(251,255)(252,256)(253,257)(254,258)
(259,263)(260,264)(261,265)(262,266)(267,271)(268,272)(269,273)(270,274)
(275,279)(276,280)(277,281)(278,282)(283,287)(284,288)(285,289)(286,290)
(291,295)(292,296)(293,297)(294,298)(299,303)(300,304)(301,305)(302,306)
(307,311)(308,312)(309,313)(310,314)(315,319)(316,320)(317,321)(318,322)
(323,327)(324,328)(325,329)(326,330)(331,335)(332,336)(333,337)(334,338)
(339,343)(340,344)(341,345)(342,346)(347,351)(348,352)(349,353)(350,354)
(355,359)(356,360)(357,361)(358,362)(363,367)(364,368)(365,369)(366,370)
(371,375)(372,376)(373,377)(374,378)(379,383)(380,384)(381,385)(382,386)
(387,391)(388,392)(389,393)(390,394)(395,399)(396,400)(397,401)(398,402);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*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(402)!(1,2);
s1 := 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);
s2 := 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);
s3 := Sym(402)!( 3, 7)( 4, 8)( 5, 9)( 6, 10)( 11, 15)( 12, 16)( 13, 17)
( 14, 18)( 19, 23)( 20, 24)( 21, 25)( 22, 26)( 27, 31)( 28, 32)( 29, 33)
( 30, 34)( 35, 39)( 36, 40)( 37, 41)( 38, 42)( 43, 47)( 44, 48)( 45, 49)
( 46, 50)( 51, 55)( 52, 56)( 53, 57)( 54, 58)( 59, 63)( 60, 64)( 61, 65)
( 62, 66)( 67, 71)( 68, 72)( 69, 73)( 70, 74)( 75, 79)( 76, 80)( 77, 81)
( 78, 82)( 83, 87)( 84, 88)( 85, 89)( 86, 90)( 91, 95)( 92, 96)( 93, 97)
( 94, 98)( 99,103)(100,104)(101,105)(102,106)(107,111)(108,112)(109,113)
(110,114)(115,119)(116,120)(117,121)(118,122)(123,127)(124,128)(125,129)
(126,130)(131,135)(132,136)(133,137)(134,138)(139,143)(140,144)(141,145)
(142,146)(147,151)(148,152)(149,153)(150,154)(155,159)(156,160)(157,161)
(158,162)(163,167)(164,168)(165,169)(166,170)(171,175)(172,176)(173,177)
(174,178)(179,183)(180,184)(181,185)(182,186)(187,191)(188,192)(189,193)
(190,194)(195,199)(196,200)(197,201)(198,202)(203,207)(204,208)(205,209)
(206,210)(211,215)(212,216)(213,217)(214,218)(219,223)(220,224)(221,225)
(222,226)(227,231)(228,232)(229,233)(230,234)(235,239)(236,240)(237,241)
(238,242)(243,247)(244,248)(245,249)(246,250)(251,255)(252,256)(253,257)
(254,258)(259,263)(260,264)(261,265)(262,266)(267,271)(268,272)(269,273)
(270,274)(275,279)(276,280)(277,281)(278,282)(283,287)(284,288)(285,289)
(286,290)(291,295)(292,296)(293,297)(294,298)(299,303)(300,304)(301,305)
(302,306)(307,311)(308,312)(309,313)(310,314)(315,319)(316,320)(317,321)
(318,322)(323,327)(324,328)(325,329)(326,330)(331,335)(332,336)(333,337)
(334,338)(339,343)(340,344)(341,345)(342,346)(347,351)(348,352)(349,353)
(350,354)(355,359)(356,360)(357,361)(358,362)(363,367)(364,368)(365,369)
(366,370)(371,375)(372,376)(373,377)(374,378)(379,383)(380,384)(381,385)
(382,386)(387,391)(388,392)(389,393)(390,394)(395,399)(396,400)(397,401)
(398,402);
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, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*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 >;
to this polytope