Polytope of Type {4,6,34}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,34}*1632b
if this polytope has a name.
Group : SmallGroup(1632,1195)
Rank : 4
Schlafli Type : {4,6,34}
Number of vertices, edges, etc : 4, 12, 102, 34
Order of s0s1s2s3 : 102
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
17-fold quotients : {4,6,2}*96c
34-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
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 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)
( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)( 63, 64)
( 67, 68)( 69,137)( 70,138)( 71,140)( 72,139)( 73,141)( 74,142)( 75,144)
( 76,143)( 77,145)( 78,146)( 79,148)( 80,147)( 81,149)( 82,150)( 83,152)
( 84,151)( 85,153)( 86,154)( 87,156)( 88,155)( 89,157)( 90,158)( 91,160)
( 92,159)( 93,161)( 94,162)( 95,164)( 96,163)( 97,165)( 98,166)( 99,168)
(100,167)(101,169)(102,170)(103,172)(104,171)(105,173)(106,174)(107,176)
(108,175)(109,177)(110,178)(111,180)(112,179)(113,181)(114,182)(115,184)
(116,183)(117,185)(118,186)(119,188)(120,187)(121,189)(122,190)(123,192)
(124,191)(125,193)(126,194)(127,196)(128,195)(129,197)(130,198)(131,200)
(132,199)(133,201)(134,202)(135,204)(136,203)(207,208)(211,212)(215,216)
(219,220)(223,224)(227,228)(231,232)(235,236)(239,240)(243,244)(247,248)
(251,252)(255,256)(259,260)(263,264)(267,268)(271,272)(273,341)(274,342)
(275,344)(276,343)(277,345)(278,346)(279,348)(280,347)(281,349)(282,350)
(283,352)(284,351)(285,353)(286,354)(287,356)(288,355)(289,357)(290,358)
(291,360)(292,359)(293,361)(294,362)(295,364)(296,363)(297,365)(298,366)
(299,368)(300,367)(301,369)(302,370)(303,372)(304,371)(305,373)(306,374)
(307,376)(308,375)(309,377)(310,378)(311,380)(312,379)(313,381)(314,382)
(315,384)(316,383)(317,385)(318,386)(319,388)(320,387)(321,389)(322,390)
(323,392)(324,391)(325,393)(326,394)(327,396)(328,395)(329,397)(330,398)
(331,400)(332,399)(333,401)(334,402)(335,404)(336,403)(337,405)(338,406)
(339,408)(340,407);;
s2 := ( 1, 69)( 2, 72)( 3, 71)( 4, 70)( 5,133)( 6,136)( 7,135)( 8,134)
( 9,129)( 10,132)( 11,131)( 12,130)( 13,125)( 14,128)( 15,127)( 16,126)
( 17,121)( 18,124)( 19,123)( 20,122)( 21,117)( 22,120)( 23,119)( 24,118)
( 25,113)( 26,116)( 27,115)( 28,114)( 29,109)( 30,112)( 31,111)( 32,110)
( 33,105)( 34,108)( 35,107)( 36,106)( 37,101)( 38,104)( 39,103)( 40,102)
( 41, 97)( 42,100)( 43, 99)( 44, 98)( 45, 93)( 46, 96)( 47, 95)( 48, 94)
( 49, 89)( 50, 92)( 51, 91)( 52, 90)( 53, 85)( 54, 88)( 55, 87)( 56, 86)
( 57, 81)( 58, 84)( 59, 83)( 60, 82)( 61, 77)( 62, 80)( 63, 79)( 64, 78)
( 65, 73)( 66, 76)( 67, 75)( 68, 74)(138,140)(141,201)(142,204)(143,203)
(144,202)(145,197)(146,200)(147,199)(148,198)(149,193)(150,196)(151,195)
(152,194)(153,189)(154,192)(155,191)(156,190)(157,185)(158,188)(159,187)
(160,186)(161,181)(162,184)(163,183)(164,182)(165,177)(166,180)(167,179)
(168,178)(169,173)(170,176)(171,175)(172,174)(205,273)(206,276)(207,275)
(208,274)(209,337)(210,340)(211,339)(212,338)(213,333)(214,336)(215,335)
(216,334)(217,329)(218,332)(219,331)(220,330)(221,325)(222,328)(223,327)
(224,326)(225,321)(226,324)(227,323)(228,322)(229,317)(230,320)(231,319)
(232,318)(233,313)(234,316)(235,315)(236,314)(237,309)(238,312)(239,311)
(240,310)(241,305)(242,308)(243,307)(244,306)(245,301)(246,304)(247,303)
(248,302)(249,297)(250,300)(251,299)(252,298)(253,293)(254,296)(255,295)
(256,294)(257,289)(258,292)(259,291)(260,290)(261,285)(262,288)(263,287)
(264,286)(265,281)(266,284)(267,283)(268,282)(269,277)(270,280)(271,279)
(272,278)(342,344)(345,405)(346,408)(347,407)(348,406)(349,401)(350,404)
(351,403)(352,402)(353,397)(354,400)(355,399)(356,398)(357,393)(358,396)
(359,395)(360,394)(361,389)(362,392)(363,391)(364,390)(365,385)(366,388)
(367,387)(368,386)(369,381)(370,384)(371,383)(372,382)(373,377)(374,380)
(375,379)(376,378);;
s3 := ( 1,209)( 2,210)( 3,211)( 4,212)( 5,205)( 6,206)( 7,207)( 8,208)
( 9,269)( 10,270)( 11,271)( 12,272)( 13,265)( 14,266)( 15,267)( 16,268)
( 17,261)( 18,262)( 19,263)( 20,264)( 21,257)( 22,258)( 23,259)( 24,260)
( 25,253)( 26,254)( 27,255)( 28,256)( 29,249)( 30,250)( 31,251)( 32,252)
( 33,245)( 34,246)( 35,247)( 36,248)( 37,241)( 38,242)( 39,243)( 40,244)
( 41,237)( 42,238)( 43,239)( 44,240)( 45,233)( 46,234)( 47,235)( 48,236)
( 49,229)( 50,230)( 51,231)( 52,232)( 53,225)( 54,226)( 55,227)( 56,228)
( 57,221)( 58,222)( 59,223)( 60,224)( 61,217)( 62,218)( 63,219)( 64,220)
( 65,213)( 66,214)( 67,215)( 68,216)( 69,277)( 70,278)( 71,279)( 72,280)
( 73,273)( 74,274)( 75,275)( 76,276)( 77,337)( 78,338)( 79,339)( 80,340)
( 81,333)( 82,334)( 83,335)( 84,336)( 85,329)( 86,330)( 87,331)( 88,332)
( 89,325)( 90,326)( 91,327)( 92,328)( 93,321)( 94,322)( 95,323)( 96,324)
( 97,317)( 98,318)( 99,319)(100,320)(101,313)(102,314)(103,315)(104,316)
(105,309)(106,310)(107,311)(108,312)(109,305)(110,306)(111,307)(112,308)
(113,301)(114,302)(115,303)(116,304)(117,297)(118,298)(119,299)(120,300)
(121,293)(122,294)(123,295)(124,296)(125,289)(126,290)(127,291)(128,292)
(129,285)(130,286)(131,287)(132,288)(133,281)(134,282)(135,283)(136,284)
(137,345)(138,346)(139,347)(140,348)(141,341)(142,342)(143,343)(144,344)
(145,405)(146,406)(147,407)(148,408)(149,401)(150,402)(151,403)(152,404)
(153,397)(154,398)(155,399)(156,400)(157,393)(158,394)(159,395)(160,396)
(161,389)(162,390)(163,391)(164,392)(165,385)(166,386)(167,387)(168,388)
(169,381)(170,382)(171,383)(172,384)(173,377)(174,378)(175,379)(176,380)
(177,373)(178,374)(179,375)(180,376)(181,369)(182,370)(183,371)(184,372)
(185,365)(186,366)(187,367)(188,368)(189,361)(190,362)(191,363)(192,364)
(193,357)(194,358)(195,359)(196,360)(197,353)(198,354)(199,355)(200,356)
(201,349)(202,350)(203,351)(204,352);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)
( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)
( 63, 64)( 67, 68)( 69,137)( 70,138)( 71,140)( 72,139)( 73,141)( 74,142)
( 75,144)( 76,143)( 77,145)( 78,146)( 79,148)( 80,147)( 81,149)( 82,150)
( 83,152)( 84,151)( 85,153)( 86,154)( 87,156)( 88,155)( 89,157)( 90,158)
( 91,160)( 92,159)( 93,161)( 94,162)( 95,164)( 96,163)( 97,165)( 98,166)
( 99,168)(100,167)(101,169)(102,170)(103,172)(104,171)(105,173)(106,174)
(107,176)(108,175)(109,177)(110,178)(111,180)(112,179)(113,181)(114,182)
(115,184)(116,183)(117,185)(118,186)(119,188)(120,187)(121,189)(122,190)
(123,192)(124,191)(125,193)(126,194)(127,196)(128,195)(129,197)(130,198)
(131,200)(132,199)(133,201)(134,202)(135,204)(136,203)(207,208)(211,212)
(215,216)(219,220)(223,224)(227,228)(231,232)(235,236)(239,240)(243,244)
(247,248)(251,252)(255,256)(259,260)(263,264)(267,268)(271,272)(273,341)
(274,342)(275,344)(276,343)(277,345)(278,346)(279,348)(280,347)(281,349)
(282,350)(283,352)(284,351)(285,353)(286,354)(287,356)(288,355)(289,357)
(290,358)(291,360)(292,359)(293,361)(294,362)(295,364)(296,363)(297,365)
(298,366)(299,368)(300,367)(301,369)(302,370)(303,372)(304,371)(305,373)
(306,374)(307,376)(308,375)(309,377)(310,378)(311,380)(312,379)(313,381)
(314,382)(315,384)(316,383)(317,385)(318,386)(319,388)(320,387)(321,389)
(322,390)(323,392)(324,391)(325,393)(326,394)(327,396)(328,395)(329,397)
(330,398)(331,400)(332,399)(333,401)(334,402)(335,404)(336,403)(337,405)
(338,406)(339,408)(340,407);
s2 := Sym(408)!( 1, 69)( 2, 72)( 3, 71)( 4, 70)( 5,133)( 6,136)( 7,135)
( 8,134)( 9,129)( 10,132)( 11,131)( 12,130)( 13,125)( 14,128)( 15,127)
( 16,126)( 17,121)( 18,124)( 19,123)( 20,122)( 21,117)( 22,120)( 23,119)
( 24,118)( 25,113)( 26,116)( 27,115)( 28,114)( 29,109)( 30,112)( 31,111)
( 32,110)( 33,105)( 34,108)( 35,107)( 36,106)( 37,101)( 38,104)( 39,103)
( 40,102)( 41, 97)( 42,100)( 43, 99)( 44, 98)( 45, 93)( 46, 96)( 47, 95)
( 48, 94)( 49, 89)( 50, 92)( 51, 91)( 52, 90)( 53, 85)( 54, 88)( 55, 87)
( 56, 86)( 57, 81)( 58, 84)( 59, 83)( 60, 82)( 61, 77)( 62, 80)( 63, 79)
( 64, 78)( 65, 73)( 66, 76)( 67, 75)( 68, 74)(138,140)(141,201)(142,204)
(143,203)(144,202)(145,197)(146,200)(147,199)(148,198)(149,193)(150,196)
(151,195)(152,194)(153,189)(154,192)(155,191)(156,190)(157,185)(158,188)
(159,187)(160,186)(161,181)(162,184)(163,183)(164,182)(165,177)(166,180)
(167,179)(168,178)(169,173)(170,176)(171,175)(172,174)(205,273)(206,276)
(207,275)(208,274)(209,337)(210,340)(211,339)(212,338)(213,333)(214,336)
(215,335)(216,334)(217,329)(218,332)(219,331)(220,330)(221,325)(222,328)
(223,327)(224,326)(225,321)(226,324)(227,323)(228,322)(229,317)(230,320)
(231,319)(232,318)(233,313)(234,316)(235,315)(236,314)(237,309)(238,312)
(239,311)(240,310)(241,305)(242,308)(243,307)(244,306)(245,301)(246,304)
(247,303)(248,302)(249,297)(250,300)(251,299)(252,298)(253,293)(254,296)
(255,295)(256,294)(257,289)(258,292)(259,291)(260,290)(261,285)(262,288)
(263,287)(264,286)(265,281)(266,284)(267,283)(268,282)(269,277)(270,280)
(271,279)(272,278)(342,344)(345,405)(346,408)(347,407)(348,406)(349,401)
(350,404)(351,403)(352,402)(353,397)(354,400)(355,399)(356,398)(357,393)
(358,396)(359,395)(360,394)(361,389)(362,392)(363,391)(364,390)(365,385)
(366,388)(367,387)(368,386)(369,381)(370,384)(371,383)(372,382)(373,377)
(374,380)(375,379)(376,378);
s3 := Sym(408)!( 1,209)( 2,210)( 3,211)( 4,212)( 5,205)( 6,206)( 7,207)
( 8,208)( 9,269)( 10,270)( 11,271)( 12,272)( 13,265)( 14,266)( 15,267)
( 16,268)( 17,261)( 18,262)( 19,263)( 20,264)( 21,257)( 22,258)( 23,259)
( 24,260)( 25,253)( 26,254)( 27,255)( 28,256)( 29,249)( 30,250)( 31,251)
( 32,252)( 33,245)( 34,246)( 35,247)( 36,248)( 37,241)( 38,242)( 39,243)
( 40,244)( 41,237)( 42,238)( 43,239)( 44,240)( 45,233)( 46,234)( 47,235)
( 48,236)( 49,229)( 50,230)( 51,231)( 52,232)( 53,225)( 54,226)( 55,227)
( 56,228)( 57,221)( 58,222)( 59,223)( 60,224)( 61,217)( 62,218)( 63,219)
( 64,220)( 65,213)( 66,214)( 67,215)( 68,216)( 69,277)( 70,278)( 71,279)
( 72,280)( 73,273)( 74,274)( 75,275)( 76,276)( 77,337)( 78,338)( 79,339)
( 80,340)( 81,333)( 82,334)( 83,335)( 84,336)( 85,329)( 86,330)( 87,331)
( 88,332)( 89,325)( 90,326)( 91,327)( 92,328)( 93,321)( 94,322)( 95,323)
( 96,324)( 97,317)( 98,318)( 99,319)(100,320)(101,313)(102,314)(103,315)
(104,316)(105,309)(106,310)(107,311)(108,312)(109,305)(110,306)(111,307)
(112,308)(113,301)(114,302)(115,303)(116,304)(117,297)(118,298)(119,299)
(120,300)(121,293)(122,294)(123,295)(124,296)(125,289)(126,290)(127,291)
(128,292)(129,285)(130,286)(131,287)(132,288)(133,281)(134,282)(135,283)
(136,284)(137,345)(138,346)(139,347)(140,348)(141,341)(142,342)(143,343)
(144,344)(145,405)(146,406)(147,407)(148,408)(149,401)(150,402)(151,403)
(152,404)(153,397)(154,398)(155,399)(156,400)(157,393)(158,394)(159,395)
(160,396)(161,389)(162,390)(163,391)(164,392)(165,385)(166,386)(167,387)
(168,388)(169,381)(170,382)(171,383)(172,384)(173,377)(174,378)(175,379)
(176,380)(177,373)(178,374)(179,375)(180,376)(181,369)(182,370)(183,371)
(184,372)(185,365)(186,366)(187,367)(188,368)(189,361)(190,362)(191,363)
(192,364)(193,357)(194,358)(195,359)(196,360)(197,353)(198,354)(199,355)
(200,356)(201,349)(202,350)(203,351)(204,352);
poly := sub<Sym(408)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope