Polytope of Type {25,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {25,4}*800
if this polytope has a name.
Group : SmallGroup(800,383)
Rank : 3
Schlafli Type : {25,4}
Number of vertices, edges, etc : 100, 200, 16
Order of s₀s₁s₂ : 25
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {25,4,2} of size 1600
Vertex Figure Of :
   {2,25,4} of size 1600
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {5,4}*160
Covers (Minimal Covers in Boldface) :
   2-fold covers : {25,8}*1600a, {25,8}*1600b, {25,4}*1600, {50,4}*1600a, {50,4}*1600b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope