Polytope of Type {8,10}

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

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