Polytope of Type {6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*768c
if this polytope has a name.
Group : SmallGroup(768,1088556)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 96, 192, 64
Order of s0s1s2 : 12
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {6,4}*384a
4-fold quotients : {6,4}*192a
8-fold quotients : {6,4}*96
16-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
32-fold quotients : {3,4}*24, {6,2}*24
64-fold quotients : {3,2}*12
96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,103)( 6,104)( 7,101)( 8,102)
( 9,108)( 10,107)( 11,106)( 12,105)( 13,110)( 14,109)( 15,112)( 16,111)
( 17,128)( 18,127)( 19,126)( 20,125)( 21,122)( 22,121)( 23,124)( 24,123)
( 25,118)( 26,117)( 27,120)( 28,119)( 29,116)( 30,115)( 31,114)( 32,113)
( 33,161)( 34,162)( 35,163)( 36,164)( 37,167)( 38,168)( 39,165)( 40,166)
( 41,172)( 42,171)( 43,170)( 44,169)( 45,174)( 46,173)( 47,176)( 48,175)
( 49,192)( 50,191)( 51,190)( 52,189)( 53,186)( 54,185)( 55,188)( 56,187)
( 57,182)( 58,181)( 59,184)( 60,183)( 61,180)( 62,179)( 63,178)( 64,177)
( 65,129)( 66,130)( 67,131)( 68,132)( 69,135)( 70,136)( 71,133)( 72,134)
( 73,140)( 74,139)( 75,138)( 76,137)( 77,142)( 78,141)( 79,144)( 80,143)
( 81,160)( 82,159)( 83,158)( 84,157)( 85,154)( 86,153)( 87,156)( 88,155)
( 89,150)( 90,149)( 91,152)( 92,151)( 93,148)( 94,147)( 95,146)( 96,145)
(193,290)(194,289)(195,292)(196,291)(197,296)(198,295)(199,294)(200,293)
(201,299)(202,300)(203,297)(204,298)(205,301)(206,302)(207,303)(208,304)
(209,319)(210,320)(211,317)(212,318)(213,313)(214,314)(215,315)(216,316)
(217,309)(218,310)(219,311)(220,312)(221,307)(222,308)(223,305)(224,306)
(225,354)(226,353)(227,356)(228,355)(229,360)(230,359)(231,358)(232,357)
(233,363)(234,364)(235,361)(236,362)(237,365)(238,366)(239,367)(240,368)
(241,383)(242,384)(243,381)(244,382)(245,377)(246,378)(247,379)(248,380)
(249,373)(250,374)(251,375)(252,376)(253,371)(254,372)(255,369)(256,370)
(257,322)(258,321)(259,324)(260,323)(261,328)(262,327)(263,326)(264,325)
(265,331)(266,332)(267,329)(268,330)(269,333)(270,334)(271,335)(272,336)
(273,351)(274,352)(275,349)(276,350)(277,345)(278,346)(279,347)(280,348)
(281,341)(282,342)(283,343)(284,344)(285,339)(286,340)(287,337)(288,338);;
s1 := ( 1, 65)( 2, 66)( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 71)( 8, 72)
( 9, 81)( 10, 82)( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 87)( 16, 88)
( 17, 73)( 18, 74)( 19, 77)( 20, 78)( 21, 75)( 22, 76)( 23, 79)( 24, 80)
( 25, 89)( 26, 90)( 27, 93)( 28, 94)( 29, 91)( 30, 92)( 31, 95)( 32, 96)
( 35, 37)( 36, 38)( 41, 49)( 42, 50)( 43, 53)( 44, 54)( 45, 51)( 46, 52)
( 47, 55)( 48, 56)( 59, 61)( 60, 62)( 97,161)( 98,162)( 99,165)(100,166)
(101,163)(102,164)(103,167)(104,168)(105,177)(106,178)(107,181)(108,182)
(109,179)(110,180)(111,183)(112,184)(113,169)(114,170)(115,173)(116,174)
(117,171)(118,172)(119,175)(120,176)(121,185)(122,186)(123,189)(124,190)
(125,187)(126,188)(127,191)(128,192)(131,133)(132,134)(137,145)(138,146)
(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(155,157)(156,158)
(193,258)(194,257)(195,262)(196,261)(197,260)(198,259)(199,264)(200,263)
(201,274)(202,273)(203,278)(204,277)(205,276)(206,275)(207,280)(208,279)
(209,266)(210,265)(211,270)(212,269)(213,268)(214,267)(215,272)(216,271)
(217,282)(218,281)(219,286)(220,285)(221,284)(222,283)(223,288)(224,287)
(225,226)(227,230)(228,229)(231,232)(233,242)(234,241)(235,246)(236,245)
(237,244)(238,243)(239,248)(240,247)(249,250)(251,254)(252,253)(255,256)
(289,354)(290,353)(291,358)(292,357)(293,356)(294,355)(295,360)(296,359)
(297,370)(298,369)(299,374)(300,373)(301,372)(302,371)(303,376)(304,375)
(305,362)(306,361)(307,366)(308,365)(309,364)(310,363)(311,368)(312,367)
(313,378)(314,377)(315,382)(316,381)(317,380)(318,379)(319,384)(320,383)
(321,322)(323,326)(324,325)(327,328)(329,338)(330,337)(331,342)(332,341)
(333,340)(334,339)(335,344)(336,343)(345,346)(347,350)(348,349)(351,352);;
s2 := ( 1,206)( 2,205)( 3,208)( 4,207)( 5,201)( 6,202)( 7,203)( 8,204)
( 9,198)( 10,197)( 11,200)( 12,199)( 13,193)( 14,194)( 15,195)( 16,196)
( 17,222)( 18,221)( 19,224)( 20,223)( 21,217)( 22,218)( 23,219)( 24,220)
( 25,214)( 26,213)( 27,216)( 28,215)( 29,209)( 30,210)( 31,211)( 32,212)
( 33,238)( 34,237)( 35,240)( 36,239)( 37,233)( 38,234)( 39,235)( 40,236)
( 41,230)( 42,229)( 43,232)( 44,231)( 45,225)( 46,226)( 47,227)( 48,228)
( 49,254)( 50,253)( 51,256)( 52,255)( 53,249)( 54,250)( 55,251)( 56,252)
( 57,246)( 58,245)( 59,248)( 60,247)( 61,241)( 62,242)( 63,243)( 64,244)
( 65,270)( 66,269)( 67,272)( 68,271)( 69,265)( 70,266)( 71,267)( 72,268)
( 73,262)( 74,261)( 75,264)( 76,263)( 77,257)( 78,258)( 79,259)( 80,260)
( 81,286)( 82,285)( 83,288)( 84,287)( 85,281)( 86,282)( 87,283)( 88,284)
( 89,278)( 90,277)( 91,280)( 92,279)( 93,273)( 94,274)( 95,275)( 96,276)
( 97,302)( 98,301)( 99,304)(100,303)(101,297)(102,298)(103,299)(104,300)
(105,294)(106,293)(107,296)(108,295)(109,289)(110,290)(111,291)(112,292)
(113,318)(114,317)(115,320)(116,319)(117,313)(118,314)(119,315)(120,316)
(121,310)(122,309)(123,312)(124,311)(125,305)(126,306)(127,307)(128,308)
(129,334)(130,333)(131,336)(132,335)(133,329)(134,330)(135,331)(136,332)
(137,326)(138,325)(139,328)(140,327)(141,321)(142,322)(143,323)(144,324)
(145,350)(146,349)(147,352)(148,351)(149,345)(150,346)(151,347)(152,348)
(153,342)(154,341)(155,344)(156,343)(157,337)(158,338)(159,339)(160,340)
(161,366)(162,365)(163,368)(164,367)(165,361)(166,362)(167,363)(168,364)
(169,358)(170,357)(171,360)(172,359)(173,353)(174,354)(175,355)(176,356)
(177,382)(178,381)(179,384)(180,383)(181,377)(182,378)(183,379)(184,380)
(185,374)(186,373)(187,376)(188,375)(189,369)(190,370)(191,371)(192,372);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,103)( 6,104)( 7,101)
( 8,102)( 9,108)( 10,107)( 11,106)( 12,105)( 13,110)( 14,109)( 15,112)
( 16,111)( 17,128)( 18,127)( 19,126)( 20,125)( 21,122)( 22,121)( 23,124)
( 24,123)( 25,118)( 26,117)( 27,120)( 28,119)( 29,116)( 30,115)( 31,114)
( 32,113)( 33,161)( 34,162)( 35,163)( 36,164)( 37,167)( 38,168)( 39,165)
( 40,166)( 41,172)( 42,171)( 43,170)( 44,169)( 45,174)( 46,173)( 47,176)
( 48,175)( 49,192)( 50,191)( 51,190)( 52,189)( 53,186)( 54,185)( 55,188)
( 56,187)( 57,182)( 58,181)( 59,184)( 60,183)( 61,180)( 62,179)( 63,178)
( 64,177)( 65,129)( 66,130)( 67,131)( 68,132)( 69,135)( 70,136)( 71,133)
( 72,134)( 73,140)( 74,139)( 75,138)( 76,137)( 77,142)( 78,141)( 79,144)
( 80,143)( 81,160)( 82,159)( 83,158)( 84,157)( 85,154)( 86,153)( 87,156)
( 88,155)( 89,150)( 90,149)( 91,152)( 92,151)( 93,148)( 94,147)( 95,146)
( 96,145)(193,290)(194,289)(195,292)(196,291)(197,296)(198,295)(199,294)
(200,293)(201,299)(202,300)(203,297)(204,298)(205,301)(206,302)(207,303)
(208,304)(209,319)(210,320)(211,317)(212,318)(213,313)(214,314)(215,315)
(216,316)(217,309)(218,310)(219,311)(220,312)(221,307)(222,308)(223,305)
(224,306)(225,354)(226,353)(227,356)(228,355)(229,360)(230,359)(231,358)
(232,357)(233,363)(234,364)(235,361)(236,362)(237,365)(238,366)(239,367)
(240,368)(241,383)(242,384)(243,381)(244,382)(245,377)(246,378)(247,379)
(248,380)(249,373)(250,374)(251,375)(252,376)(253,371)(254,372)(255,369)
(256,370)(257,322)(258,321)(259,324)(260,323)(261,328)(262,327)(263,326)
(264,325)(265,331)(266,332)(267,329)(268,330)(269,333)(270,334)(271,335)
(272,336)(273,351)(274,352)(275,349)(276,350)(277,345)(278,346)(279,347)
(280,348)(281,341)(282,342)(283,343)(284,344)(285,339)(286,340)(287,337)
(288,338);
s1 := Sym(384)!( 1, 65)( 2, 66)( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 71)
( 8, 72)( 9, 81)( 10, 82)( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 87)
( 16, 88)( 17, 73)( 18, 74)( 19, 77)( 20, 78)( 21, 75)( 22, 76)( 23, 79)
( 24, 80)( 25, 89)( 26, 90)( 27, 93)( 28, 94)( 29, 91)( 30, 92)( 31, 95)
( 32, 96)( 35, 37)( 36, 38)( 41, 49)( 42, 50)( 43, 53)( 44, 54)( 45, 51)
( 46, 52)( 47, 55)( 48, 56)( 59, 61)( 60, 62)( 97,161)( 98,162)( 99,165)
(100,166)(101,163)(102,164)(103,167)(104,168)(105,177)(106,178)(107,181)
(108,182)(109,179)(110,180)(111,183)(112,184)(113,169)(114,170)(115,173)
(116,174)(117,171)(118,172)(119,175)(120,176)(121,185)(122,186)(123,189)
(124,190)(125,187)(126,188)(127,191)(128,192)(131,133)(132,134)(137,145)
(138,146)(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(155,157)
(156,158)(193,258)(194,257)(195,262)(196,261)(197,260)(198,259)(199,264)
(200,263)(201,274)(202,273)(203,278)(204,277)(205,276)(206,275)(207,280)
(208,279)(209,266)(210,265)(211,270)(212,269)(213,268)(214,267)(215,272)
(216,271)(217,282)(218,281)(219,286)(220,285)(221,284)(222,283)(223,288)
(224,287)(225,226)(227,230)(228,229)(231,232)(233,242)(234,241)(235,246)
(236,245)(237,244)(238,243)(239,248)(240,247)(249,250)(251,254)(252,253)
(255,256)(289,354)(290,353)(291,358)(292,357)(293,356)(294,355)(295,360)
(296,359)(297,370)(298,369)(299,374)(300,373)(301,372)(302,371)(303,376)
(304,375)(305,362)(306,361)(307,366)(308,365)(309,364)(310,363)(311,368)
(312,367)(313,378)(314,377)(315,382)(316,381)(317,380)(318,379)(319,384)
(320,383)(321,322)(323,326)(324,325)(327,328)(329,338)(330,337)(331,342)
(332,341)(333,340)(334,339)(335,344)(336,343)(345,346)(347,350)(348,349)
(351,352);
s2 := Sym(384)!( 1,206)( 2,205)( 3,208)( 4,207)( 5,201)( 6,202)( 7,203)
( 8,204)( 9,198)( 10,197)( 11,200)( 12,199)( 13,193)( 14,194)( 15,195)
( 16,196)( 17,222)( 18,221)( 19,224)( 20,223)( 21,217)( 22,218)( 23,219)
( 24,220)( 25,214)( 26,213)( 27,216)( 28,215)( 29,209)( 30,210)( 31,211)
( 32,212)( 33,238)( 34,237)( 35,240)( 36,239)( 37,233)( 38,234)( 39,235)
( 40,236)( 41,230)( 42,229)( 43,232)( 44,231)( 45,225)( 46,226)( 47,227)
( 48,228)( 49,254)( 50,253)( 51,256)( 52,255)( 53,249)( 54,250)( 55,251)
( 56,252)( 57,246)( 58,245)( 59,248)( 60,247)( 61,241)( 62,242)( 63,243)
( 64,244)( 65,270)( 66,269)( 67,272)( 68,271)( 69,265)( 70,266)( 71,267)
( 72,268)( 73,262)( 74,261)( 75,264)( 76,263)( 77,257)( 78,258)( 79,259)
( 80,260)( 81,286)( 82,285)( 83,288)( 84,287)( 85,281)( 86,282)( 87,283)
( 88,284)( 89,278)( 90,277)( 91,280)( 92,279)( 93,273)( 94,274)( 95,275)
( 96,276)( 97,302)( 98,301)( 99,304)(100,303)(101,297)(102,298)(103,299)
(104,300)(105,294)(106,293)(107,296)(108,295)(109,289)(110,290)(111,291)
(112,292)(113,318)(114,317)(115,320)(116,319)(117,313)(118,314)(119,315)
(120,316)(121,310)(122,309)(123,312)(124,311)(125,305)(126,306)(127,307)
(128,308)(129,334)(130,333)(131,336)(132,335)(133,329)(134,330)(135,331)
(136,332)(137,326)(138,325)(139,328)(140,327)(141,321)(142,322)(143,323)
(144,324)(145,350)(146,349)(147,352)(148,351)(149,345)(150,346)(151,347)
(152,348)(153,342)(154,341)(155,344)(156,343)(157,337)(158,338)(159,339)
(160,340)(161,366)(162,365)(163,368)(164,367)(165,361)(166,362)(167,363)
(168,364)(169,358)(170,357)(171,360)(172,359)(173,353)(174,354)(175,355)
(176,356)(177,382)(178,381)(179,384)(180,383)(181,377)(182,378)(183,379)
(184,380)(185,374)(186,373)(187,376)(188,375)(189,369)(190,370)(191,371)
(192,372);
poly := sub<Sym(384)|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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0 >;
References : None.
to this polytope