Polytope of Type {32,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,8}*512d
if this polytope has a name.
Group : SmallGroup(512,58716)
Rank : 3
Schlafli Type : {32,8}
Number of vertices, edges, etc : 32, 128, 8
Order of s0s1s2 : 32
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {16,8}*256d, {32,4}*256b
4-fold quotients : {8,8}*128b, {16,4}*128a
8-fold quotients : {4,8}*64a, {8,4}*64a, {16,2}*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 := ( 1,193)( 2,194)( 3,196)( 4,195)( 5,197)( 6,198)( 7,200)( 8,199)
( 9,203)( 10,204)( 11,201)( 12,202)( 13,207)( 14,208)( 15,205)( 16,206)
( 17,210)( 18,209)( 19,211)( 20,212)( 21,214)( 22,213)( 23,215)( 24,216)
( 25,220)( 26,219)( 27,218)( 28,217)( 29,224)( 30,223)( 31,222)( 32,221)
( 33,237)( 34,238)( 35,240)( 36,239)( 37,233)( 38,234)( 39,236)( 40,235)
( 41,229)( 42,230)( 43,232)( 44,231)( 45,225)( 46,226)( 47,228)( 48,227)
( 49,254)( 50,253)( 51,255)( 52,256)( 53,250)( 54,249)( 55,251)( 56,252)
( 57,246)( 58,245)( 59,247)( 60,248)( 61,242)( 62,241)( 63,243)( 64,244)
( 65,129)( 66,130)( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)
( 73,139)( 74,140)( 75,137)( 76,138)( 77,143)( 78,144)( 79,141)( 80,142)
( 81,146)( 82,145)( 83,147)( 84,148)( 85,150)( 86,149)( 87,151)( 88,152)
( 89,156)( 90,155)( 91,154)( 92,153)( 93,160)( 94,159)( 95,158)( 96,157)
( 97,173)( 98,174)( 99,176)(100,175)(101,169)(102,170)(103,172)(104,171)
(105,165)(106,166)(107,168)(108,167)(109,161)(110,162)(111,164)(112,163)
(113,190)(114,189)(115,191)(116,192)(117,186)(118,185)(119,187)(120,188)
(121,182)(122,181)(123,183)(124,184)(125,178)(126,177)(127,179)(128,180)
(257,449)(258,450)(259,452)(260,451)(261,453)(262,454)(263,456)(264,455)
(265,459)(266,460)(267,457)(268,458)(269,463)(270,464)(271,461)(272,462)
(273,466)(274,465)(275,467)(276,468)(277,470)(278,469)(279,471)(280,472)
(281,476)(282,475)(283,474)(284,473)(285,480)(286,479)(287,478)(288,477)
(289,493)(290,494)(291,496)(292,495)(293,489)(294,490)(295,492)(296,491)
(297,485)(298,486)(299,488)(300,487)(301,481)(302,482)(303,484)(304,483)
(305,510)(306,509)(307,511)(308,512)(309,506)(310,505)(311,507)(312,508)
(313,502)(314,501)(315,503)(316,504)(317,498)(318,497)(319,499)(320,500)
(321,385)(322,386)(323,388)(324,387)(325,389)(326,390)(327,392)(328,391)
(329,395)(330,396)(331,393)(332,394)(333,399)(334,400)(335,397)(336,398)
(337,402)(338,401)(339,403)(340,404)(341,406)(342,405)(343,407)(344,408)
(345,412)(346,411)(347,410)(348,409)(349,416)(350,415)(351,414)(352,413)
(353,429)(354,430)(355,432)(356,431)(357,425)(358,426)(359,428)(360,427)
(361,421)(362,422)(363,424)(364,423)(365,417)(366,418)(367,420)(368,419)
(369,446)(370,445)(371,447)(372,448)(373,442)(374,441)(375,443)(376,444)
(377,438)(378,437)(379,439)(380,440)(381,434)(382,433)(383,435)(384,436);;
s1 := ( 1,257)( 2,258)( 3,260)( 4,259)( 5,261)( 6,262)( 7,264)( 8,263)
( 9,267)( 10,268)( 11,265)( 12,266)( 13,271)( 14,272)( 15,269)( 16,270)
( 17,278)( 18,277)( 19,279)( 20,280)( 21,274)( 22,273)( 23,275)( 24,276)
( 25,288)( 26,287)( 27,286)( 28,285)( 29,284)( 30,283)( 31,282)( 32,281)
( 33,297)( 34,298)( 35,300)( 36,299)( 37,301)( 38,302)( 39,304)( 40,303)
( 41,289)( 42,290)( 43,292)( 44,291)( 45,293)( 46,294)( 47,296)( 48,295)
( 49,318)( 50,317)( 51,319)( 52,320)( 53,314)( 54,313)( 55,315)( 56,316)
( 57,310)( 58,309)( 59,311)( 60,312)( 61,306)( 62,305)( 63,307)( 64,308)
( 65,337)( 66,338)( 67,340)( 68,339)( 69,341)( 70,342)( 71,344)( 72,343)
( 73,347)( 74,348)( 75,345)( 76,346)( 77,351)( 78,352)( 79,349)( 80,350)
( 81,321)( 82,322)( 83,324)( 84,323)( 85,325)( 86,326)( 87,328)( 88,327)
( 89,331)( 90,332)( 91,329)( 92,330)( 93,335)( 94,336)( 95,333)( 96,334)
( 97,377)( 98,378)( 99,380)(100,379)(101,381)(102,382)(103,384)(104,383)
(105,369)(106,370)(107,372)(108,371)(109,373)(110,374)(111,376)(112,375)
(113,361)(114,362)(115,364)(116,363)(117,365)(118,366)(119,368)(120,367)
(121,353)(122,354)(123,356)(124,355)(125,357)(126,358)(127,360)(128,359)
(129,417)(130,418)(131,420)(132,419)(133,421)(134,422)(135,424)(136,423)
(137,427)(138,428)(139,425)(140,426)(141,431)(142,432)(143,429)(144,430)
(145,438)(146,437)(147,439)(148,440)(149,434)(150,433)(151,435)(152,436)
(153,448)(154,447)(155,446)(156,445)(157,444)(158,443)(159,442)(160,441)
(161,385)(162,386)(163,388)(164,387)(165,389)(166,390)(167,392)(168,391)
(169,395)(170,396)(171,393)(172,394)(173,399)(174,400)(175,397)(176,398)
(177,406)(178,405)(179,407)(180,408)(181,402)(182,401)(183,403)(184,404)
(185,416)(186,415)(187,414)(188,413)(189,412)(190,411)(191,410)(192,409)
(193,501)(194,502)(195,504)(196,503)(197,497)(198,498)(199,500)(200,499)
(201,511)(202,512)(203,509)(204,510)(205,507)(206,508)(207,505)(208,506)
(209,485)(210,486)(211,488)(212,487)(213,481)(214,482)(215,484)(216,483)
(217,495)(218,496)(219,493)(220,494)(221,491)(222,492)(223,489)(224,490)
(225,469)(226,470)(227,472)(228,471)(229,465)(230,466)(231,468)(232,467)
(233,479)(234,480)(235,477)(236,478)(237,475)(238,476)(239,473)(240,474)
(241,453)(242,454)(243,456)(244,455)(245,449)(246,450)(247,452)(248,451)
(249,463)(250,464)(251,461)(252,462)(253,459)(254,460)(255,457)(256,458);;
s2 := ( 1, 65)( 2, 66)( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 71)( 8, 72)
( 9, 73)( 10, 74)( 11, 75)( 12, 76)( 13, 77)( 14, 78)( 15, 79)( 16, 80)
( 17, 86)( 18, 85)( 19, 88)( 20, 87)( 21, 82)( 22, 81)( 23, 84)( 24, 83)
( 25, 94)( 26, 93)( 27, 96)( 28, 95)( 29, 90)( 30, 89)( 31, 92)( 32, 91)
( 33,101)( 34,102)( 35,103)( 36,104)( 37, 97)( 38, 98)( 39, 99)( 40,100)
( 41,109)( 42,110)( 43,111)( 44,112)( 45,105)( 46,106)( 47,107)( 48,108)
( 49,114)( 50,113)( 51,116)( 52,115)( 53,118)( 54,117)( 55,120)( 56,119)
( 57,122)( 58,121)( 59,124)( 60,123)( 61,126)( 62,125)( 63,128)( 64,127)
(129,193)(130,194)(131,195)(132,196)(133,197)(134,198)(135,199)(136,200)
(137,201)(138,202)(139,203)(140,204)(141,205)(142,206)(143,207)(144,208)
(145,214)(146,213)(147,216)(148,215)(149,210)(150,209)(151,212)(152,211)
(153,222)(154,221)(155,224)(156,223)(157,218)(158,217)(159,220)(160,219)
(161,229)(162,230)(163,231)(164,232)(165,225)(166,226)(167,227)(168,228)
(169,237)(170,238)(171,239)(172,240)(173,233)(174,234)(175,235)(176,236)
(177,242)(178,241)(179,244)(180,243)(181,246)(182,245)(183,248)(184,247)
(185,250)(186,249)(187,252)(188,251)(189,254)(190,253)(191,256)(192,255)
(257,321)(258,322)(259,323)(260,324)(261,325)(262,326)(263,327)(264,328)
(265,329)(266,330)(267,331)(268,332)(269,333)(270,334)(271,335)(272,336)
(273,342)(274,341)(275,344)(276,343)(277,338)(278,337)(279,340)(280,339)
(281,350)(282,349)(283,352)(284,351)(285,346)(286,345)(287,348)(288,347)
(289,357)(290,358)(291,359)(292,360)(293,353)(294,354)(295,355)(296,356)
(297,365)(298,366)(299,367)(300,368)(301,361)(302,362)(303,363)(304,364)
(305,370)(306,369)(307,372)(308,371)(309,374)(310,373)(311,376)(312,375)
(313,378)(314,377)(315,380)(316,379)(317,382)(318,381)(319,384)(320,383)
(385,449)(386,450)(387,451)(388,452)(389,453)(390,454)(391,455)(392,456)
(393,457)(394,458)(395,459)(396,460)(397,461)(398,462)(399,463)(400,464)
(401,470)(402,469)(403,472)(404,471)(405,466)(406,465)(407,468)(408,467)
(409,478)(410,477)(411,480)(412,479)(413,474)(414,473)(415,476)(416,475)
(417,485)(418,486)(419,487)(420,488)(421,481)(422,482)(423,483)(424,484)
(425,493)(426,494)(427,495)(428,496)(429,489)(430,490)(431,491)(432,492)
(433,498)(434,497)(435,500)(436,499)(437,502)(438,501)(439,504)(440,503)
(441,506)(442,505)(443,508)(444,507)(445,510)(446,509)(447,512)(448,511);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s2*s1*s0*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(512)!( 1,193)( 2,194)( 3,196)( 4,195)( 5,197)( 6,198)( 7,200)
( 8,199)( 9,203)( 10,204)( 11,201)( 12,202)( 13,207)( 14,208)( 15,205)
( 16,206)( 17,210)( 18,209)( 19,211)( 20,212)( 21,214)( 22,213)( 23,215)
( 24,216)( 25,220)( 26,219)( 27,218)( 28,217)( 29,224)( 30,223)( 31,222)
( 32,221)( 33,237)( 34,238)( 35,240)( 36,239)( 37,233)( 38,234)( 39,236)
( 40,235)( 41,229)( 42,230)( 43,232)( 44,231)( 45,225)( 46,226)( 47,228)
( 48,227)( 49,254)( 50,253)( 51,255)( 52,256)( 53,250)( 54,249)( 55,251)
( 56,252)( 57,246)( 58,245)( 59,247)( 60,248)( 61,242)( 62,241)( 63,243)
( 64,244)( 65,129)( 66,130)( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)
( 72,135)( 73,139)( 74,140)( 75,137)( 76,138)( 77,143)( 78,144)( 79,141)
( 80,142)( 81,146)( 82,145)( 83,147)( 84,148)( 85,150)( 86,149)( 87,151)
( 88,152)( 89,156)( 90,155)( 91,154)( 92,153)( 93,160)( 94,159)( 95,158)
( 96,157)( 97,173)( 98,174)( 99,176)(100,175)(101,169)(102,170)(103,172)
(104,171)(105,165)(106,166)(107,168)(108,167)(109,161)(110,162)(111,164)
(112,163)(113,190)(114,189)(115,191)(116,192)(117,186)(118,185)(119,187)
(120,188)(121,182)(122,181)(123,183)(124,184)(125,178)(126,177)(127,179)
(128,180)(257,449)(258,450)(259,452)(260,451)(261,453)(262,454)(263,456)
(264,455)(265,459)(266,460)(267,457)(268,458)(269,463)(270,464)(271,461)
(272,462)(273,466)(274,465)(275,467)(276,468)(277,470)(278,469)(279,471)
(280,472)(281,476)(282,475)(283,474)(284,473)(285,480)(286,479)(287,478)
(288,477)(289,493)(290,494)(291,496)(292,495)(293,489)(294,490)(295,492)
(296,491)(297,485)(298,486)(299,488)(300,487)(301,481)(302,482)(303,484)
(304,483)(305,510)(306,509)(307,511)(308,512)(309,506)(310,505)(311,507)
(312,508)(313,502)(314,501)(315,503)(316,504)(317,498)(318,497)(319,499)
(320,500)(321,385)(322,386)(323,388)(324,387)(325,389)(326,390)(327,392)
(328,391)(329,395)(330,396)(331,393)(332,394)(333,399)(334,400)(335,397)
(336,398)(337,402)(338,401)(339,403)(340,404)(341,406)(342,405)(343,407)
(344,408)(345,412)(346,411)(347,410)(348,409)(349,416)(350,415)(351,414)
(352,413)(353,429)(354,430)(355,432)(356,431)(357,425)(358,426)(359,428)
(360,427)(361,421)(362,422)(363,424)(364,423)(365,417)(366,418)(367,420)
(368,419)(369,446)(370,445)(371,447)(372,448)(373,442)(374,441)(375,443)
(376,444)(377,438)(378,437)(379,439)(380,440)(381,434)(382,433)(383,435)
(384,436);
s1 := Sym(512)!( 1,257)( 2,258)( 3,260)( 4,259)( 5,261)( 6,262)( 7,264)
( 8,263)( 9,267)( 10,268)( 11,265)( 12,266)( 13,271)( 14,272)( 15,269)
( 16,270)( 17,278)( 18,277)( 19,279)( 20,280)( 21,274)( 22,273)( 23,275)
( 24,276)( 25,288)( 26,287)( 27,286)( 28,285)( 29,284)( 30,283)( 31,282)
( 32,281)( 33,297)( 34,298)( 35,300)( 36,299)( 37,301)( 38,302)( 39,304)
( 40,303)( 41,289)( 42,290)( 43,292)( 44,291)( 45,293)( 46,294)( 47,296)
( 48,295)( 49,318)( 50,317)( 51,319)( 52,320)( 53,314)( 54,313)( 55,315)
( 56,316)( 57,310)( 58,309)( 59,311)( 60,312)( 61,306)( 62,305)( 63,307)
( 64,308)( 65,337)( 66,338)( 67,340)( 68,339)( 69,341)( 70,342)( 71,344)
( 72,343)( 73,347)( 74,348)( 75,345)( 76,346)( 77,351)( 78,352)( 79,349)
( 80,350)( 81,321)( 82,322)( 83,324)( 84,323)( 85,325)( 86,326)( 87,328)
( 88,327)( 89,331)( 90,332)( 91,329)( 92,330)( 93,335)( 94,336)( 95,333)
( 96,334)( 97,377)( 98,378)( 99,380)(100,379)(101,381)(102,382)(103,384)
(104,383)(105,369)(106,370)(107,372)(108,371)(109,373)(110,374)(111,376)
(112,375)(113,361)(114,362)(115,364)(116,363)(117,365)(118,366)(119,368)
(120,367)(121,353)(122,354)(123,356)(124,355)(125,357)(126,358)(127,360)
(128,359)(129,417)(130,418)(131,420)(132,419)(133,421)(134,422)(135,424)
(136,423)(137,427)(138,428)(139,425)(140,426)(141,431)(142,432)(143,429)
(144,430)(145,438)(146,437)(147,439)(148,440)(149,434)(150,433)(151,435)
(152,436)(153,448)(154,447)(155,446)(156,445)(157,444)(158,443)(159,442)
(160,441)(161,385)(162,386)(163,388)(164,387)(165,389)(166,390)(167,392)
(168,391)(169,395)(170,396)(171,393)(172,394)(173,399)(174,400)(175,397)
(176,398)(177,406)(178,405)(179,407)(180,408)(181,402)(182,401)(183,403)
(184,404)(185,416)(186,415)(187,414)(188,413)(189,412)(190,411)(191,410)
(192,409)(193,501)(194,502)(195,504)(196,503)(197,497)(198,498)(199,500)
(200,499)(201,511)(202,512)(203,509)(204,510)(205,507)(206,508)(207,505)
(208,506)(209,485)(210,486)(211,488)(212,487)(213,481)(214,482)(215,484)
(216,483)(217,495)(218,496)(219,493)(220,494)(221,491)(222,492)(223,489)
(224,490)(225,469)(226,470)(227,472)(228,471)(229,465)(230,466)(231,468)
(232,467)(233,479)(234,480)(235,477)(236,478)(237,475)(238,476)(239,473)
(240,474)(241,453)(242,454)(243,456)(244,455)(245,449)(246,450)(247,452)
(248,451)(249,463)(250,464)(251,461)(252,462)(253,459)(254,460)(255,457)
(256,458);
s2 := Sym(512)!( 1, 65)( 2, 66)( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 71)
( 8, 72)( 9, 73)( 10, 74)( 11, 75)( 12, 76)( 13, 77)( 14, 78)( 15, 79)
( 16, 80)( 17, 86)( 18, 85)( 19, 88)( 20, 87)( 21, 82)( 22, 81)( 23, 84)
( 24, 83)( 25, 94)( 26, 93)( 27, 96)( 28, 95)( 29, 90)( 30, 89)( 31, 92)
( 32, 91)( 33,101)( 34,102)( 35,103)( 36,104)( 37, 97)( 38, 98)( 39, 99)
( 40,100)( 41,109)( 42,110)( 43,111)( 44,112)( 45,105)( 46,106)( 47,107)
( 48,108)( 49,114)( 50,113)( 51,116)( 52,115)( 53,118)( 54,117)( 55,120)
( 56,119)( 57,122)( 58,121)( 59,124)( 60,123)( 61,126)( 62,125)( 63,128)
( 64,127)(129,193)(130,194)(131,195)(132,196)(133,197)(134,198)(135,199)
(136,200)(137,201)(138,202)(139,203)(140,204)(141,205)(142,206)(143,207)
(144,208)(145,214)(146,213)(147,216)(148,215)(149,210)(150,209)(151,212)
(152,211)(153,222)(154,221)(155,224)(156,223)(157,218)(158,217)(159,220)
(160,219)(161,229)(162,230)(163,231)(164,232)(165,225)(166,226)(167,227)
(168,228)(169,237)(170,238)(171,239)(172,240)(173,233)(174,234)(175,235)
(176,236)(177,242)(178,241)(179,244)(180,243)(181,246)(182,245)(183,248)
(184,247)(185,250)(186,249)(187,252)(188,251)(189,254)(190,253)(191,256)
(192,255)(257,321)(258,322)(259,323)(260,324)(261,325)(262,326)(263,327)
(264,328)(265,329)(266,330)(267,331)(268,332)(269,333)(270,334)(271,335)
(272,336)(273,342)(274,341)(275,344)(276,343)(277,338)(278,337)(279,340)
(280,339)(281,350)(282,349)(283,352)(284,351)(285,346)(286,345)(287,348)
(288,347)(289,357)(290,358)(291,359)(292,360)(293,353)(294,354)(295,355)
(296,356)(297,365)(298,366)(299,367)(300,368)(301,361)(302,362)(303,363)
(304,364)(305,370)(306,369)(307,372)(308,371)(309,374)(310,373)(311,376)
(312,375)(313,378)(314,377)(315,380)(316,379)(317,382)(318,381)(319,384)
(320,383)(385,449)(386,450)(387,451)(388,452)(389,453)(390,454)(391,455)
(392,456)(393,457)(394,458)(395,459)(396,460)(397,461)(398,462)(399,463)
(400,464)(401,470)(402,469)(403,472)(404,471)(405,466)(406,465)(407,468)
(408,467)(409,478)(410,477)(411,480)(412,479)(413,474)(414,473)(415,476)
(416,475)(417,485)(418,486)(419,487)(420,488)(421,481)(422,482)(423,483)
(424,484)(425,493)(426,494)(427,495)(428,496)(429,489)(430,490)(431,491)
(432,492)(433,498)(434,497)(435,500)(436,499)(437,502)(438,501)(439,504)
(440,503)(441,506)(442,505)(443,508)(444,507)(445,510)(446,509)(447,512)
(448,511);
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s2*s1*s0*s1*s0*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 >;
References : None.
to this polytope