Polytope of Type {4,102}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,102}*816b
if this polytope has a name.
Group : SmallGroup(816,195)
Rank : 3
Schlafli Type : {4,102}
Number of vertices, edges, etc : 4, 204, 102
Order of s0s1s2 : 102
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,102,2} of size 1632
Vertex Figure Of :
{2,4,102} of size 1632
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,51}*408
17-fold quotients : {4,6}*48c
34-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,204}*1632b, {4,204}*1632c, {4,102}*1632
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408);;
s1 := ( 2, 3)( 5, 65)( 6, 67)( 7, 66)( 8, 68)( 9, 61)( 10, 63)( 11, 62)
( 12, 64)( 13, 57)( 14, 59)( 15, 58)( 16, 60)( 17, 53)( 18, 55)( 19, 54)
( 20, 56)( 21, 49)( 22, 51)( 23, 50)( 24, 52)( 25, 45)( 26, 47)( 27, 46)
( 28, 48)( 29, 41)( 30, 43)( 31, 42)( 32, 44)( 33, 37)( 34, 39)( 35, 38)
( 36, 40)( 69,137)( 70,139)( 71,138)( 72,140)( 73,201)( 74,203)( 75,202)
( 76,204)( 77,197)( 78,199)( 79,198)( 80,200)( 81,193)( 82,195)( 83,194)
( 84,196)( 85,189)( 86,191)( 87,190)( 88,192)( 89,185)( 90,187)( 91,186)
( 92,188)( 93,181)( 94,183)( 95,182)( 96,184)( 97,177)( 98,179)( 99,178)
(100,180)(101,173)(102,175)(103,174)(104,176)(105,169)(106,171)(107,170)
(108,172)(109,165)(110,167)(111,166)(112,168)(113,161)(114,163)(115,162)
(116,164)(117,157)(118,159)(119,158)(120,160)(121,153)(122,155)(123,154)
(124,156)(125,149)(126,151)(127,150)(128,152)(129,145)(130,147)(131,146)
(132,148)(133,141)(134,143)(135,142)(136,144)(206,207)(209,269)(210,271)
(211,270)(212,272)(213,265)(214,267)(215,266)(216,268)(217,261)(218,263)
(219,262)(220,264)(221,257)(222,259)(223,258)(224,260)(225,253)(226,255)
(227,254)(228,256)(229,249)(230,251)(231,250)(232,252)(233,245)(234,247)
(235,246)(236,248)(237,241)(238,243)(239,242)(240,244)(273,341)(274,343)
(275,342)(276,344)(277,405)(278,407)(279,406)(280,408)(281,401)(282,403)
(283,402)(284,404)(285,397)(286,399)(287,398)(288,400)(289,393)(290,395)
(291,394)(292,396)(293,389)(294,391)(295,390)(296,392)(297,385)(298,387)
(299,386)(300,388)(301,381)(302,383)(303,382)(304,384)(305,377)(306,379)
(307,378)(308,380)(309,373)(310,375)(311,374)(312,376)(313,369)(314,371)
(315,370)(316,372)(317,365)(318,367)(319,366)(320,368)(321,361)(322,363)
(323,362)(324,364)(325,357)(326,359)(327,358)(328,360)(329,353)(330,355)
(331,354)(332,356)(333,349)(334,351)(335,350)(336,352)(337,345)(338,347)
(339,346)(340,348);;
s2 := ( 1,345)( 2,348)( 3,347)( 4,346)( 5,341)( 6,344)( 7,343)( 8,342)
( 9,405)( 10,408)( 11,407)( 12,406)( 13,401)( 14,404)( 15,403)( 16,402)
( 17,397)( 18,400)( 19,399)( 20,398)( 21,393)( 22,396)( 23,395)( 24,394)
( 25,389)( 26,392)( 27,391)( 28,390)( 29,385)( 30,388)( 31,387)( 32,386)
( 33,381)( 34,384)( 35,383)( 36,382)( 37,377)( 38,380)( 39,379)( 40,378)
( 41,373)( 42,376)( 43,375)( 44,374)( 45,369)( 46,372)( 47,371)( 48,370)
( 49,365)( 50,368)( 51,367)( 52,366)( 53,361)( 54,364)( 55,363)( 56,362)
( 57,357)( 58,360)( 59,359)( 60,358)( 61,353)( 62,356)( 63,355)( 64,354)
( 65,349)( 66,352)( 67,351)( 68,350)( 69,277)( 70,280)( 71,279)( 72,278)
( 73,273)( 74,276)( 75,275)( 76,274)( 77,337)( 78,340)( 79,339)( 80,338)
( 81,333)( 82,336)( 83,335)( 84,334)( 85,329)( 86,332)( 87,331)( 88,330)
( 89,325)( 90,328)( 91,327)( 92,326)( 93,321)( 94,324)( 95,323)( 96,322)
( 97,317)( 98,320)( 99,319)(100,318)(101,313)(102,316)(103,315)(104,314)
(105,309)(106,312)(107,311)(108,310)(109,305)(110,308)(111,307)(112,306)
(113,301)(114,304)(115,303)(116,302)(117,297)(118,300)(119,299)(120,298)
(121,293)(122,296)(123,295)(124,294)(125,289)(126,292)(127,291)(128,290)
(129,285)(130,288)(131,287)(132,286)(133,281)(134,284)(135,283)(136,282)
(137,209)(138,212)(139,211)(140,210)(141,205)(142,208)(143,207)(144,206)
(145,269)(146,272)(147,271)(148,270)(149,265)(150,268)(151,267)(152,266)
(153,261)(154,264)(155,263)(156,262)(157,257)(158,260)(159,259)(160,258)
(161,253)(162,256)(163,255)(164,254)(165,249)(166,252)(167,251)(168,250)
(169,245)(170,248)(171,247)(172,246)(173,241)(174,244)(175,243)(176,242)
(177,237)(178,240)(179,239)(180,238)(181,233)(182,236)(183,235)(184,234)
(185,229)(186,232)(187,231)(188,230)(189,225)(190,228)(191,227)(192,226)
(193,221)(194,224)(195,223)(196,222)(197,217)(198,220)(199,219)(200,218)
(201,213)(202,216)(203,215)(204,214);;
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(408)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408);
s1 := Sym(408)!( 2, 3)( 5, 65)( 6, 67)( 7, 66)( 8, 68)( 9, 61)( 10, 63)
( 11, 62)( 12, 64)( 13, 57)( 14, 59)( 15, 58)( 16, 60)( 17, 53)( 18, 55)
( 19, 54)( 20, 56)( 21, 49)( 22, 51)( 23, 50)( 24, 52)( 25, 45)( 26, 47)
( 27, 46)( 28, 48)( 29, 41)( 30, 43)( 31, 42)( 32, 44)( 33, 37)( 34, 39)
( 35, 38)( 36, 40)( 69,137)( 70,139)( 71,138)( 72,140)( 73,201)( 74,203)
( 75,202)( 76,204)( 77,197)( 78,199)( 79,198)( 80,200)( 81,193)( 82,195)
( 83,194)( 84,196)( 85,189)( 86,191)( 87,190)( 88,192)( 89,185)( 90,187)
( 91,186)( 92,188)( 93,181)( 94,183)( 95,182)( 96,184)( 97,177)( 98,179)
( 99,178)(100,180)(101,173)(102,175)(103,174)(104,176)(105,169)(106,171)
(107,170)(108,172)(109,165)(110,167)(111,166)(112,168)(113,161)(114,163)
(115,162)(116,164)(117,157)(118,159)(119,158)(120,160)(121,153)(122,155)
(123,154)(124,156)(125,149)(126,151)(127,150)(128,152)(129,145)(130,147)
(131,146)(132,148)(133,141)(134,143)(135,142)(136,144)(206,207)(209,269)
(210,271)(211,270)(212,272)(213,265)(214,267)(215,266)(216,268)(217,261)
(218,263)(219,262)(220,264)(221,257)(222,259)(223,258)(224,260)(225,253)
(226,255)(227,254)(228,256)(229,249)(230,251)(231,250)(232,252)(233,245)
(234,247)(235,246)(236,248)(237,241)(238,243)(239,242)(240,244)(273,341)
(274,343)(275,342)(276,344)(277,405)(278,407)(279,406)(280,408)(281,401)
(282,403)(283,402)(284,404)(285,397)(286,399)(287,398)(288,400)(289,393)
(290,395)(291,394)(292,396)(293,389)(294,391)(295,390)(296,392)(297,385)
(298,387)(299,386)(300,388)(301,381)(302,383)(303,382)(304,384)(305,377)
(306,379)(307,378)(308,380)(309,373)(310,375)(311,374)(312,376)(313,369)
(314,371)(315,370)(316,372)(317,365)(318,367)(319,366)(320,368)(321,361)
(322,363)(323,362)(324,364)(325,357)(326,359)(327,358)(328,360)(329,353)
(330,355)(331,354)(332,356)(333,349)(334,351)(335,350)(336,352)(337,345)
(338,347)(339,346)(340,348);
s2 := Sym(408)!( 1,345)( 2,348)( 3,347)( 4,346)( 5,341)( 6,344)( 7,343)
( 8,342)( 9,405)( 10,408)( 11,407)( 12,406)( 13,401)( 14,404)( 15,403)
( 16,402)( 17,397)( 18,400)( 19,399)( 20,398)( 21,393)( 22,396)( 23,395)
( 24,394)( 25,389)( 26,392)( 27,391)( 28,390)( 29,385)( 30,388)( 31,387)
( 32,386)( 33,381)( 34,384)( 35,383)( 36,382)( 37,377)( 38,380)( 39,379)
( 40,378)( 41,373)( 42,376)( 43,375)( 44,374)( 45,369)( 46,372)( 47,371)
( 48,370)( 49,365)( 50,368)( 51,367)( 52,366)( 53,361)( 54,364)( 55,363)
( 56,362)( 57,357)( 58,360)( 59,359)( 60,358)( 61,353)( 62,356)( 63,355)
( 64,354)( 65,349)( 66,352)( 67,351)( 68,350)( 69,277)( 70,280)( 71,279)
( 72,278)( 73,273)( 74,276)( 75,275)( 76,274)( 77,337)( 78,340)( 79,339)
( 80,338)( 81,333)( 82,336)( 83,335)( 84,334)( 85,329)( 86,332)( 87,331)
( 88,330)( 89,325)( 90,328)( 91,327)( 92,326)( 93,321)( 94,324)( 95,323)
( 96,322)( 97,317)( 98,320)( 99,319)(100,318)(101,313)(102,316)(103,315)
(104,314)(105,309)(106,312)(107,311)(108,310)(109,305)(110,308)(111,307)
(112,306)(113,301)(114,304)(115,303)(116,302)(117,297)(118,300)(119,299)
(120,298)(121,293)(122,296)(123,295)(124,294)(125,289)(126,292)(127,291)
(128,290)(129,285)(130,288)(131,287)(132,286)(133,281)(134,284)(135,283)
(136,282)(137,209)(138,212)(139,211)(140,210)(141,205)(142,208)(143,207)
(144,206)(145,269)(146,272)(147,271)(148,270)(149,265)(150,268)(151,267)
(152,266)(153,261)(154,264)(155,263)(156,262)(157,257)(158,260)(159,259)
(160,258)(161,253)(162,256)(163,255)(164,254)(165,249)(166,252)(167,251)
(168,250)(169,245)(170,248)(171,247)(172,246)(173,241)(174,244)(175,243)
(176,242)(177,237)(178,240)(179,239)(180,238)(181,233)(182,236)(183,235)
(184,234)(185,229)(186,232)(187,231)(188,230)(189,225)(190,228)(191,227)
(192,226)(193,221)(194,224)(195,223)(196,222)(197,217)(198,220)(199,219)
(200,218)(201,213)(202,216)(203,215)(204,214);
poly := sub<Sym(408)|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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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