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Polytope of Type {8,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,16}*512f
if this polytope has a name.
Group : SmallGroup(512,32843)
Rank : 3
Schlafli Type : {8,16}
Number of vertices, edges, etc : 16, 128, 32
Order of s0s1s2 : 16
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,8}*256a, {8,16}*256a, {8,16}*256b
   4-fold quotients : {4,8}*128a, {8,4}*128a, {8,8}*128a, {8,8}*128b, {8,8}*128c, {8,8}*128d
   8-fold quotients : {4,8}*64a, {8,4}*64a, {4,8}*64b, {8,4}*64b, {4,4}*64
   16-fold quotients : {4,4}*32, {2,8}*32, {8,2}*32
   32-fold quotients : {2,4}*16, {4,2}*16
   64-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 65)(  2, 66)(  3, 67)(  4, 68)(  5, 70)(  6, 69)(  7, 72)(  8, 71)
(  9, 74)( 10, 73)( 11, 76)( 12, 75)( 13, 77)( 14, 78)( 15, 79)( 16, 80)
( 17, 83)( 18, 84)( 19, 81)( 20, 82)( 21, 88)( 22, 87)( 23, 86)( 24, 85)
( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 95)( 30, 96)( 31, 93)( 32, 94)
( 33,101)( 34,102)( 35,103)( 36,104)( 37, 97)( 38, 98)( 39, 99)( 40,100)
( 41,110)( 42,109)( 43,112)( 44,111)( 45,106)( 46,105)( 47,108)( 48,107)
( 49,119)( 50,120)( 51,117)( 52,118)( 53,115)( 54,116)( 55,113)( 56,114)
( 57,128)( 58,127)( 59,126)( 60,125)( 61,124)( 62,123)( 63,122)( 64,121)
(129,193)(130,194)(131,195)(132,196)(133,198)(134,197)(135,200)(136,199)
(137,202)(138,201)(139,204)(140,203)(141,205)(142,206)(143,207)(144,208)
(145,211)(146,212)(147,209)(148,210)(149,216)(150,215)(151,214)(152,213)
(153,220)(154,219)(155,218)(156,217)(157,223)(158,224)(159,221)(160,222)
(161,229)(162,230)(163,231)(164,232)(165,225)(166,226)(167,227)(168,228)
(169,238)(170,237)(171,240)(172,239)(173,234)(174,233)(175,236)(176,235)
(177,247)(178,248)(179,245)(180,246)(181,243)(182,244)(183,241)(184,242)
(185,256)(186,255)(187,254)(188,253)(189,252)(190,251)(191,250)(192,249)
(257,321)(258,322)(259,323)(260,324)(261,326)(262,325)(263,328)(264,327)
(265,330)(266,329)(267,332)(268,331)(269,333)(270,334)(271,335)(272,336)
(273,339)(274,340)(275,337)(276,338)(277,344)(278,343)(279,342)(280,341)
(281,348)(282,347)(283,346)(284,345)(285,351)(286,352)(287,349)(288,350)
(289,357)(290,358)(291,359)(292,360)(293,353)(294,354)(295,355)(296,356)
(297,366)(298,365)(299,368)(300,367)(301,362)(302,361)(303,364)(304,363)
(305,375)(306,376)(307,373)(308,374)(309,371)(310,372)(311,369)(312,370)
(313,384)(314,383)(315,382)(316,381)(317,380)(318,379)(319,378)(320,377)
(385,449)(386,450)(387,451)(388,452)(389,454)(390,453)(391,456)(392,455)
(393,458)(394,457)(395,460)(396,459)(397,461)(398,462)(399,463)(400,464)
(401,467)(402,468)(403,465)(404,466)(405,472)(406,471)(407,470)(408,469)
(409,476)(410,475)(411,474)(412,473)(413,479)(414,480)(415,477)(416,478)
(417,485)(418,486)(419,487)(420,488)(421,481)(422,482)(423,483)(424,484)
(425,494)(426,493)(427,496)(428,495)(429,490)(430,489)(431,492)(432,491)
(433,503)(434,504)(435,501)(436,502)(437,499)(438,500)(439,497)(440,498)
(441,512)(442,511)(443,510)(444,509)(445,508)(446,507)(447,506)(448,505);;
s1 := (  1,257)(  2,258)(  3,259)(  4,260)(  5,262)(  6,261)(  7,264)(  8,263)
(  9,266)( 10,265)( 11,268)( 12,267)( 13,269)( 14,270)( 15,271)( 16,272)
( 17,275)( 18,276)( 19,273)( 20,274)( 21,280)( 22,279)( 23,278)( 24,277)
( 25,284)( 26,283)( 27,282)( 28,281)( 29,287)( 30,288)( 31,285)( 32,286)
( 33,297)( 34,298)( 35,299)( 36,300)( 37,302)( 38,301)( 39,304)( 40,303)
( 41,289)( 42,290)( 43,291)( 44,292)( 45,294)( 46,293)( 47,296)( 48,295)
( 49,315)( 50,316)( 51,313)( 52,314)( 53,320)( 54,319)( 55,318)( 56,317)
( 57,307)( 58,308)( 59,305)( 60,306)( 61,312)( 62,311)( 63,310)( 64,309)
( 65,337)( 66,338)( 67,339)( 68,340)( 69,342)( 70,341)( 71,344)( 72,343)
( 73,346)( 74,345)( 75,348)( 76,347)( 77,349)( 78,350)( 79,351)( 80,352)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,326)( 86,325)( 87,328)( 88,327)
( 89,330)( 90,329)( 91,332)( 92,331)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,377)( 98,378)( 99,379)(100,380)(101,382)(102,381)(103,384)(104,383)
(105,369)(106,370)(107,371)(108,372)(109,374)(110,373)(111,376)(112,375)
(113,361)(114,362)(115,363)(116,364)(117,366)(118,365)(119,368)(120,367)
(121,353)(122,354)(123,355)(124,356)(125,358)(126,357)(127,360)(128,359)
(129,417)(130,418)(131,419)(132,420)(133,422)(134,421)(135,424)(136,423)
(137,426)(138,425)(139,428)(140,427)(141,429)(142,430)(143,431)(144,432)
(145,435)(146,436)(147,433)(148,434)(149,440)(150,439)(151,438)(152,437)
(153,444)(154,443)(155,442)(156,441)(157,447)(158,448)(159,445)(160,446)
(161,385)(162,386)(163,387)(164,388)(165,390)(166,389)(167,392)(168,391)
(169,394)(170,393)(171,396)(172,395)(173,397)(174,398)(175,399)(176,400)
(177,403)(178,404)(179,401)(180,402)(181,408)(182,407)(183,406)(184,405)
(185,412)(186,411)(187,410)(188,409)(189,415)(190,416)(191,413)(192,414)
(193,501)(194,502)(195,503)(196,504)(197,497)(198,498)(199,499)(200,500)
(201,510)(202,509)(203,512)(204,511)(205,506)(206,505)(207,508)(208,507)
(209,485)(210,486)(211,487)(212,488)(213,481)(214,482)(215,483)(216,484)
(217,494)(218,493)(219,496)(220,495)(221,490)(222,489)(223,492)(224,491)
(225,469)(226,470)(227,471)(228,472)(229,465)(230,466)(231,467)(232,468)
(233,478)(234,477)(235,480)(236,479)(237,474)(238,473)(239,476)(240,475)
(241,453)(242,454)(243,455)(244,456)(245,449)(246,450)(247,451)(248,452)
(249,462)(250,461)(251,464)(252,463)(253,458)(254,457)(255,460)(256,459);;
s2 := (  1,129)(  2,130)(  3,132)(  4,131)(  5,134)(  6,133)(  7,135)(  8,136)
(  9,138)( 10,137)( 11,139)( 12,140)( 13,141)( 14,142)( 15,144)( 16,143)
( 17,149)( 18,150)( 19,152)( 20,151)( 21,145)( 22,146)( 23,148)( 24,147)
( 25,158)( 26,157)( 27,159)( 28,160)( 29,154)( 30,153)( 31,155)( 32,156)
( 33,169)( 34,170)( 35,172)( 36,171)( 37,174)( 38,173)( 39,175)( 40,176)
( 41,161)( 42,162)( 43,164)( 44,163)( 45,166)( 46,165)( 47,167)( 48,168)
( 49,189)( 50,190)( 51,192)( 52,191)( 53,185)( 54,186)( 55,188)( 56,187)
( 57,181)( 58,182)( 59,184)( 60,183)( 61,177)( 62,178)( 63,180)( 64,179)
( 65,193)( 66,194)( 67,196)( 68,195)( 69,198)( 70,197)( 71,199)( 72,200)
( 73,202)( 74,201)( 75,203)( 76,204)( 77,205)( 78,206)( 79,208)( 80,207)
( 81,213)( 82,214)( 83,216)( 84,215)( 85,209)( 86,210)( 87,212)( 88,211)
( 89,222)( 90,221)( 91,223)( 92,224)( 93,218)( 94,217)( 95,219)( 96,220)
( 97,233)( 98,234)( 99,236)(100,235)(101,238)(102,237)(103,239)(104,240)
(105,225)(106,226)(107,228)(108,227)(109,230)(110,229)(111,231)(112,232)
(113,253)(114,254)(115,256)(116,255)(117,249)(118,250)(119,252)(120,251)
(121,245)(122,246)(123,248)(124,247)(125,241)(126,242)(127,244)(128,243)
(257,385)(258,386)(259,388)(260,387)(261,390)(262,389)(263,391)(264,392)
(265,394)(266,393)(267,395)(268,396)(269,397)(270,398)(271,400)(272,399)
(273,405)(274,406)(275,408)(276,407)(277,401)(278,402)(279,404)(280,403)
(281,414)(282,413)(283,415)(284,416)(285,410)(286,409)(287,411)(288,412)
(289,425)(290,426)(291,428)(292,427)(293,430)(294,429)(295,431)(296,432)
(297,417)(298,418)(299,420)(300,419)(301,422)(302,421)(303,423)(304,424)
(305,445)(306,446)(307,448)(308,447)(309,441)(310,442)(311,444)(312,443)
(313,437)(314,438)(315,440)(316,439)(317,433)(318,434)(319,436)(320,435)
(321,449)(322,450)(323,452)(324,451)(325,454)(326,453)(327,455)(328,456)
(329,458)(330,457)(331,459)(332,460)(333,461)(334,462)(335,464)(336,463)
(337,469)(338,470)(339,472)(340,471)(341,465)(342,466)(343,468)(344,467)
(345,478)(346,477)(347,479)(348,480)(349,474)(350,473)(351,475)(352,476)
(353,489)(354,490)(355,492)(356,491)(357,494)(358,493)(359,495)(360,496)
(361,481)(362,482)(363,484)(364,483)(365,486)(366,485)(367,487)(368,488)
(369,509)(370,510)(371,512)(372,511)(373,505)(374,506)(375,508)(376,507)
(377,501)(378,502)(379,504)(380,503)(381,497)(382,498)(383,500)(384,499);;
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*s1*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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(512)!(  1, 65)(  2, 66)(  3, 67)(  4, 68)(  5, 70)(  6, 69)(  7, 72)
(  8, 71)(  9, 74)( 10, 73)( 11, 76)( 12, 75)( 13, 77)( 14, 78)( 15, 79)
( 16, 80)( 17, 83)( 18, 84)( 19, 81)( 20, 82)( 21, 88)( 22, 87)( 23, 86)
( 24, 85)( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 95)( 30, 96)( 31, 93)
( 32, 94)( 33,101)( 34,102)( 35,103)( 36,104)( 37, 97)( 38, 98)( 39, 99)
( 40,100)( 41,110)( 42,109)( 43,112)( 44,111)( 45,106)( 46,105)( 47,108)
( 48,107)( 49,119)( 50,120)( 51,117)( 52,118)( 53,115)( 54,116)( 55,113)
( 56,114)( 57,128)( 58,127)( 59,126)( 60,125)( 61,124)( 62,123)( 63,122)
( 64,121)(129,193)(130,194)(131,195)(132,196)(133,198)(134,197)(135,200)
(136,199)(137,202)(138,201)(139,204)(140,203)(141,205)(142,206)(143,207)
(144,208)(145,211)(146,212)(147,209)(148,210)(149,216)(150,215)(151,214)
(152,213)(153,220)(154,219)(155,218)(156,217)(157,223)(158,224)(159,221)
(160,222)(161,229)(162,230)(163,231)(164,232)(165,225)(166,226)(167,227)
(168,228)(169,238)(170,237)(171,240)(172,239)(173,234)(174,233)(175,236)
(176,235)(177,247)(178,248)(179,245)(180,246)(181,243)(182,244)(183,241)
(184,242)(185,256)(186,255)(187,254)(188,253)(189,252)(190,251)(191,250)
(192,249)(257,321)(258,322)(259,323)(260,324)(261,326)(262,325)(263,328)
(264,327)(265,330)(266,329)(267,332)(268,331)(269,333)(270,334)(271,335)
(272,336)(273,339)(274,340)(275,337)(276,338)(277,344)(278,343)(279,342)
(280,341)(281,348)(282,347)(283,346)(284,345)(285,351)(286,352)(287,349)
(288,350)(289,357)(290,358)(291,359)(292,360)(293,353)(294,354)(295,355)
(296,356)(297,366)(298,365)(299,368)(300,367)(301,362)(302,361)(303,364)
(304,363)(305,375)(306,376)(307,373)(308,374)(309,371)(310,372)(311,369)
(312,370)(313,384)(314,383)(315,382)(316,381)(317,380)(318,379)(319,378)
(320,377)(385,449)(386,450)(387,451)(388,452)(389,454)(390,453)(391,456)
(392,455)(393,458)(394,457)(395,460)(396,459)(397,461)(398,462)(399,463)
(400,464)(401,467)(402,468)(403,465)(404,466)(405,472)(406,471)(407,470)
(408,469)(409,476)(410,475)(411,474)(412,473)(413,479)(414,480)(415,477)
(416,478)(417,485)(418,486)(419,487)(420,488)(421,481)(422,482)(423,483)
(424,484)(425,494)(426,493)(427,496)(428,495)(429,490)(430,489)(431,492)
(432,491)(433,503)(434,504)(435,501)(436,502)(437,499)(438,500)(439,497)
(440,498)(441,512)(442,511)(443,510)(444,509)(445,508)(446,507)(447,506)
(448,505);
s1 := Sym(512)!(  1,257)(  2,258)(  3,259)(  4,260)(  5,262)(  6,261)(  7,264)
(  8,263)(  9,266)( 10,265)( 11,268)( 12,267)( 13,269)( 14,270)( 15,271)
( 16,272)( 17,275)( 18,276)( 19,273)( 20,274)( 21,280)( 22,279)( 23,278)
( 24,277)( 25,284)( 26,283)( 27,282)( 28,281)( 29,287)( 30,288)( 31,285)
( 32,286)( 33,297)( 34,298)( 35,299)( 36,300)( 37,302)( 38,301)( 39,304)
( 40,303)( 41,289)( 42,290)( 43,291)( 44,292)( 45,294)( 46,293)( 47,296)
( 48,295)( 49,315)( 50,316)( 51,313)( 52,314)( 53,320)( 54,319)( 55,318)
( 56,317)( 57,307)( 58,308)( 59,305)( 60,306)( 61,312)( 62,311)( 63,310)
( 64,309)( 65,337)( 66,338)( 67,339)( 68,340)( 69,342)( 70,341)( 71,344)
( 72,343)( 73,346)( 74,345)( 75,348)( 76,347)( 77,349)( 78,350)( 79,351)
( 80,352)( 81,321)( 82,322)( 83,323)( 84,324)( 85,326)( 86,325)( 87,328)
( 88,327)( 89,330)( 90,329)( 91,332)( 92,331)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,377)( 98,378)( 99,379)(100,380)(101,382)(102,381)(103,384)
(104,383)(105,369)(106,370)(107,371)(108,372)(109,374)(110,373)(111,376)
(112,375)(113,361)(114,362)(115,363)(116,364)(117,366)(118,365)(119,368)
(120,367)(121,353)(122,354)(123,355)(124,356)(125,358)(126,357)(127,360)
(128,359)(129,417)(130,418)(131,419)(132,420)(133,422)(134,421)(135,424)
(136,423)(137,426)(138,425)(139,428)(140,427)(141,429)(142,430)(143,431)
(144,432)(145,435)(146,436)(147,433)(148,434)(149,440)(150,439)(151,438)
(152,437)(153,444)(154,443)(155,442)(156,441)(157,447)(158,448)(159,445)
(160,446)(161,385)(162,386)(163,387)(164,388)(165,390)(166,389)(167,392)
(168,391)(169,394)(170,393)(171,396)(172,395)(173,397)(174,398)(175,399)
(176,400)(177,403)(178,404)(179,401)(180,402)(181,408)(182,407)(183,406)
(184,405)(185,412)(186,411)(187,410)(188,409)(189,415)(190,416)(191,413)
(192,414)(193,501)(194,502)(195,503)(196,504)(197,497)(198,498)(199,499)
(200,500)(201,510)(202,509)(203,512)(204,511)(205,506)(206,505)(207,508)
(208,507)(209,485)(210,486)(211,487)(212,488)(213,481)(214,482)(215,483)
(216,484)(217,494)(218,493)(219,496)(220,495)(221,490)(222,489)(223,492)
(224,491)(225,469)(226,470)(227,471)(228,472)(229,465)(230,466)(231,467)
(232,468)(233,478)(234,477)(235,480)(236,479)(237,474)(238,473)(239,476)
(240,475)(241,453)(242,454)(243,455)(244,456)(245,449)(246,450)(247,451)
(248,452)(249,462)(250,461)(251,464)(252,463)(253,458)(254,457)(255,460)
(256,459);
s2 := Sym(512)!(  1,129)(  2,130)(  3,132)(  4,131)(  5,134)(  6,133)(  7,135)
(  8,136)(  9,138)( 10,137)( 11,139)( 12,140)( 13,141)( 14,142)( 15,144)
( 16,143)( 17,149)( 18,150)( 19,152)( 20,151)( 21,145)( 22,146)( 23,148)
( 24,147)( 25,158)( 26,157)( 27,159)( 28,160)( 29,154)( 30,153)( 31,155)
( 32,156)( 33,169)( 34,170)( 35,172)( 36,171)( 37,174)( 38,173)( 39,175)
( 40,176)( 41,161)( 42,162)( 43,164)( 44,163)( 45,166)( 46,165)( 47,167)
( 48,168)( 49,189)( 50,190)( 51,192)( 52,191)( 53,185)( 54,186)( 55,188)
( 56,187)( 57,181)( 58,182)( 59,184)( 60,183)( 61,177)( 62,178)( 63,180)
( 64,179)( 65,193)( 66,194)( 67,196)( 68,195)( 69,198)( 70,197)( 71,199)
( 72,200)( 73,202)( 74,201)( 75,203)( 76,204)( 77,205)( 78,206)( 79,208)
( 80,207)( 81,213)( 82,214)( 83,216)( 84,215)( 85,209)( 86,210)( 87,212)
( 88,211)( 89,222)( 90,221)( 91,223)( 92,224)( 93,218)( 94,217)( 95,219)
( 96,220)( 97,233)( 98,234)( 99,236)(100,235)(101,238)(102,237)(103,239)
(104,240)(105,225)(106,226)(107,228)(108,227)(109,230)(110,229)(111,231)
(112,232)(113,253)(114,254)(115,256)(116,255)(117,249)(118,250)(119,252)
(120,251)(121,245)(122,246)(123,248)(124,247)(125,241)(126,242)(127,244)
(128,243)(257,385)(258,386)(259,388)(260,387)(261,390)(262,389)(263,391)
(264,392)(265,394)(266,393)(267,395)(268,396)(269,397)(270,398)(271,400)
(272,399)(273,405)(274,406)(275,408)(276,407)(277,401)(278,402)(279,404)
(280,403)(281,414)(282,413)(283,415)(284,416)(285,410)(286,409)(287,411)
(288,412)(289,425)(290,426)(291,428)(292,427)(293,430)(294,429)(295,431)
(296,432)(297,417)(298,418)(299,420)(300,419)(301,422)(302,421)(303,423)
(304,424)(305,445)(306,446)(307,448)(308,447)(309,441)(310,442)(311,444)
(312,443)(313,437)(314,438)(315,440)(316,439)(317,433)(318,434)(319,436)
(320,435)(321,449)(322,450)(323,452)(324,451)(325,454)(326,453)(327,455)
(328,456)(329,458)(330,457)(331,459)(332,460)(333,461)(334,462)(335,464)
(336,463)(337,469)(338,470)(339,472)(340,471)(341,465)(342,466)(343,468)
(344,467)(345,478)(346,477)(347,479)(348,480)(349,474)(350,473)(351,475)
(352,476)(353,489)(354,490)(355,492)(356,491)(357,494)(358,493)(359,495)
(360,496)(361,481)(362,482)(363,484)(364,483)(365,486)(366,485)(367,487)
(368,488)(369,509)(370,510)(371,512)(372,511)(373,505)(374,506)(375,508)
(376,507)(377,501)(378,502)(379,504)(380,503)(381,497)(382,498)(383,500)
(384,499);
poly := sub<Sym(512)|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*s1*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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 >; 
 
References : None.
to this polytope