Polytope of Type {10,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8}*800
if this polytope has a name.
Group : SmallGroup(800,1042)
Rank : 3
Schlafli Type : {10,8}
Number of vertices, edges, etc : 50, 200, 40
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,8,2} of size 1600
Vertex Figure Of :
   {2,10,8} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,4}*400
   4-fold quotients : {10,4}*200
   25-fold quotients : {2,8}*32
   50-fold quotients : {2,4}*16
   100-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,16}*1600, {20,8}*1600a
Permutation Representation (GAP) :

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