Polytope of Type {96,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {96,4}*768b
if this polytope has a name.
Group : SmallGroup(768,90243)
Rank : 3
Schlafli Type : {96,4}
Number of vertices, edges, etc : 96, 192, 4
Order of s0s1s2 : 96
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
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 : {48,4}*384a
3-fold quotients : {32,4}*256b
4-fold quotients : {24,4}*192a, {48,2}*192
6-fold quotients : {16,4}*128a
8-fold quotients : {12,4}*96a, {24,2}*96
12-fold quotients : {8,4}*64a, {16,2}*64
16-fold quotients : {12,2}*48, {6,4}*48a
24-fold quotients : {4,4}*32, {8,2}*32
32-fold quotients : {6,2}*24
48-fold quotients : {2,4}*16, {4,2}*16
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 := ( 1,193)( 2,195)( 3,194)( 4,196)( 5,198)( 6,197)( 7,202)( 8,204)
( 9,203)( 10,199)( 11,201)( 12,200)( 13,211)( 14,213)( 15,212)( 16,214)
( 17,216)( 18,215)( 19,205)( 20,207)( 21,206)( 22,208)( 23,210)( 24,209)
( 25,220)( 26,222)( 27,221)( 28,217)( 29,219)( 30,218)( 31,223)( 32,225)
( 33,224)( 34,226)( 35,228)( 36,227)( 37,238)( 38,240)( 39,239)( 40,235)
( 41,237)( 42,236)( 43,232)( 44,234)( 45,233)( 46,229)( 47,231)( 48,230)
( 49,253)( 50,255)( 51,254)( 52,256)( 53,258)( 54,257)( 55,262)( 56,264)
( 57,263)( 58,259)( 59,261)( 60,260)( 61,241)( 62,243)( 63,242)( 64,244)
( 65,246)( 66,245)( 67,250)( 68,252)( 69,251)( 70,247)( 71,249)( 72,248)
( 73,280)( 74,282)( 75,281)( 76,277)( 77,279)( 78,278)( 79,283)( 80,285)
( 81,284)( 82,286)( 83,288)( 84,287)( 85,268)( 86,270)( 87,269)( 88,265)
( 89,267)( 90,266)( 91,271)( 92,273)( 93,272)( 94,274)( 95,276)( 96,275)
( 97,289)( 98,291)( 99,290)(100,292)(101,294)(102,293)(103,298)(104,300)
(105,299)(106,295)(107,297)(108,296)(109,307)(110,309)(111,308)(112,310)
(113,312)(114,311)(115,301)(116,303)(117,302)(118,304)(119,306)(120,305)
(121,316)(122,318)(123,317)(124,313)(125,315)(126,314)(127,319)(128,321)
(129,320)(130,322)(131,324)(132,323)(133,334)(134,336)(135,335)(136,331)
(137,333)(138,332)(139,328)(140,330)(141,329)(142,325)(143,327)(144,326)
(145,349)(146,351)(147,350)(148,352)(149,354)(150,353)(151,358)(152,360)
(153,359)(154,355)(155,357)(156,356)(157,337)(158,339)(159,338)(160,340)
(161,342)(162,341)(163,346)(164,348)(165,347)(166,343)(167,345)(168,344)
(169,376)(170,378)(171,377)(172,373)(173,375)(174,374)(175,379)(176,381)
(177,380)(178,382)(179,384)(180,383)(181,364)(182,366)(183,365)(184,361)
(185,363)(186,362)(187,367)(188,369)(189,368)(190,370)(191,372)(192,371);;
s1 := ( 1, 3)( 4, 6)( 7, 12)( 8, 11)( 9, 10)( 13, 21)( 14, 20)( 15, 19)
( 16, 24)( 17, 23)( 18, 22)( 25, 27)( 28, 30)( 31, 36)( 32, 35)( 33, 34)
( 37, 45)( 38, 44)( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 49, 63)( 50, 62)
( 51, 61)( 52, 66)( 53, 65)( 54, 64)( 55, 72)( 56, 71)( 57, 70)( 58, 69)
( 59, 68)( 60, 67)( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)
( 79, 96)( 80, 95)( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 97,123)( 98,122)
( 99,121)(100,126)(101,125)(102,124)(103,132)(104,131)(105,130)(106,129)
(107,128)(108,127)(109,141)(110,140)(111,139)(112,144)(113,143)(114,142)
(115,135)(116,134)(117,133)(118,138)(119,137)(120,136)(145,183)(146,182)
(147,181)(148,186)(149,185)(150,184)(151,192)(152,191)(153,190)(154,189)
(155,188)(156,187)(157,171)(158,170)(159,169)(160,174)(161,173)(162,172)
(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(193,243)(194,242)
(195,241)(196,246)(197,245)(198,244)(199,252)(200,251)(201,250)(202,249)
(203,248)(204,247)(205,261)(206,260)(207,259)(208,264)(209,263)(210,262)
(211,255)(212,254)(213,253)(214,258)(215,257)(216,256)(217,267)(218,266)
(219,265)(220,270)(221,269)(222,268)(223,276)(224,275)(225,274)(226,273)
(227,272)(228,271)(229,285)(230,284)(231,283)(232,288)(233,287)(234,286)
(235,279)(236,278)(237,277)(238,282)(239,281)(240,280)(289,366)(290,365)
(291,364)(292,363)(293,362)(294,361)(295,369)(296,368)(297,367)(298,372)
(299,371)(300,370)(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)
(307,378)(308,377)(309,376)(310,375)(311,374)(312,373)(313,342)(314,341)
(315,340)(316,339)(317,338)(318,337)(319,345)(320,344)(321,343)(322,348)
(323,347)(324,346)(325,360)(326,359)(327,358)(328,357)(329,356)(330,355)
(331,354)(332,353)(333,352)(334,351)(335,350)(336,349);;
s2 := ( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)
( 9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)( 16,112)
( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)( 24,120)
( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)
( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)( 48,144)
( 49,148)( 50,149)( 51,150)( 52,145)( 53,146)( 54,147)( 55,154)( 56,155)
( 57,156)( 58,151)( 59,152)( 60,153)( 61,160)( 62,161)( 63,162)( 64,157)
( 65,158)( 66,159)( 67,166)( 68,167)( 69,168)( 70,163)( 71,164)( 72,165)
( 73,172)( 74,173)( 75,174)( 76,169)( 77,170)( 78,171)( 79,178)( 80,179)
( 81,180)( 82,175)( 83,176)( 84,177)( 85,184)( 86,185)( 87,186)( 88,181)
( 89,182)( 90,183)( 91,190)( 92,191)( 93,192)( 94,187)( 95,188)( 96,189)
(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)(200,296)
(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)(208,304)
(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)(216,312)
(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)(224,320)
(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)(232,328)
(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)(240,336)
(241,340)(242,341)(243,342)(244,337)(245,338)(246,339)(247,346)(248,347)
(249,348)(250,343)(251,344)(252,345)(253,352)(254,353)(255,354)(256,349)
(257,350)(258,351)(259,358)(260,359)(261,360)(262,355)(263,356)(264,357)
(265,364)(266,365)(267,366)(268,361)(269,362)(270,363)(271,370)(272,371)
(273,372)(274,367)(275,368)(276,369)(277,376)(278,377)(279,378)(280,373)
(281,374)(282,375)(283,382)(284,383)(285,384)(286,379)(287,380)(288,381);;
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*s2*s1*s2*s1*s0*s1*s0*s2*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s0*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(384)!( 1,193)( 2,195)( 3,194)( 4,196)( 5,198)( 6,197)( 7,202)
( 8,204)( 9,203)( 10,199)( 11,201)( 12,200)( 13,211)( 14,213)( 15,212)
( 16,214)( 17,216)( 18,215)( 19,205)( 20,207)( 21,206)( 22,208)( 23,210)
( 24,209)( 25,220)( 26,222)( 27,221)( 28,217)( 29,219)( 30,218)( 31,223)
( 32,225)( 33,224)( 34,226)( 35,228)( 36,227)( 37,238)( 38,240)( 39,239)
( 40,235)( 41,237)( 42,236)( 43,232)( 44,234)( 45,233)( 46,229)( 47,231)
( 48,230)( 49,253)( 50,255)( 51,254)( 52,256)( 53,258)( 54,257)( 55,262)
( 56,264)( 57,263)( 58,259)( 59,261)( 60,260)( 61,241)( 62,243)( 63,242)
( 64,244)( 65,246)( 66,245)( 67,250)( 68,252)( 69,251)( 70,247)( 71,249)
( 72,248)( 73,280)( 74,282)( 75,281)( 76,277)( 77,279)( 78,278)( 79,283)
( 80,285)( 81,284)( 82,286)( 83,288)( 84,287)( 85,268)( 86,270)( 87,269)
( 88,265)( 89,267)( 90,266)( 91,271)( 92,273)( 93,272)( 94,274)( 95,276)
( 96,275)( 97,289)( 98,291)( 99,290)(100,292)(101,294)(102,293)(103,298)
(104,300)(105,299)(106,295)(107,297)(108,296)(109,307)(110,309)(111,308)
(112,310)(113,312)(114,311)(115,301)(116,303)(117,302)(118,304)(119,306)
(120,305)(121,316)(122,318)(123,317)(124,313)(125,315)(126,314)(127,319)
(128,321)(129,320)(130,322)(131,324)(132,323)(133,334)(134,336)(135,335)
(136,331)(137,333)(138,332)(139,328)(140,330)(141,329)(142,325)(143,327)
(144,326)(145,349)(146,351)(147,350)(148,352)(149,354)(150,353)(151,358)
(152,360)(153,359)(154,355)(155,357)(156,356)(157,337)(158,339)(159,338)
(160,340)(161,342)(162,341)(163,346)(164,348)(165,347)(166,343)(167,345)
(168,344)(169,376)(170,378)(171,377)(172,373)(173,375)(174,374)(175,379)
(176,381)(177,380)(178,382)(179,384)(180,383)(181,364)(182,366)(183,365)
(184,361)(185,363)(186,362)(187,367)(188,369)(189,368)(190,370)(191,372)
(192,371);
s1 := Sym(384)!( 1, 3)( 4, 6)( 7, 12)( 8, 11)( 9, 10)( 13, 21)( 14, 20)
( 15, 19)( 16, 24)( 17, 23)( 18, 22)( 25, 27)( 28, 30)( 31, 36)( 32, 35)
( 33, 34)( 37, 45)( 38, 44)( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 49, 63)
( 50, 62)( 51, 61)( 52, 66)( 53, 65)( 54, 64)( 55, 72)( 56, 71)( 57, 70)
( 58, 69)( 59, 68)( 60, 67)( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)
( 78, 88)( 79, 96)( 80, 95)( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 97,123)
( 98,122)( 99,121)(100,126)(101,125)(102,124)(103,132)(104,131)(105,130)
(106,129)(107,128)(108,127)(109,141)(110,140)(111,139)(112,144)(113,143)
(114,142)(115,135)(116,134)(117,133)(118,138)(119,137)(120,136)(145,183)
(146,182)(147,181)(148,186)(149,185)(150,184)(151,192)(152,191)(153,190)
(154,189)(155,188)(156,187)(157,171)(158,170)(159,169)(160,174)(161,173)
(162,172)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(193,243)
(194,242)(195,241)(196,246)(197,245)(198,244)(199,252)(200,251)(201,250)
(202,249)(203,248)(204,247)(205,261)(206,260)(207,259)(208,264)(209,263)
(210,262)(211,255)(212,254)(213,253)(214,258)(215,257)(216,256)(217,267)
(218,266)(219,265)(220,270)(221,269)(222,268)(223,276)(224,275)(225,274)
(226,273)(227,272)(228,271)(229,285)(230,284)(231,283)(232,288)(233,287)
(234,286)(235,279)(236,278)(237,277)(238,282)(239,281)(240,280)(289,366)
(290,365)(291,364)(292,363)(293,362)(294,361)(295,369)(296,368)(297,367)
(298,372)(299,371)(300,370)(301,384)(302,383)(303,382)(304,381)(305,380)
(306,379)(307,378)(308,377)(309,376)(310,375)(311,374)(312,373)(313,342)
(314,341)(315,340)(316,339)(317,338)(318,337)(319,345)(320,344)(321,343)
(322,348)(323,347)(324,346)(325,360)(326,359)(327,358)(328,357)(329,356)
(330,355)(331,354)(332,353)(333,352)(334,351)(335,350)(336,349);
s2 := Sym(384)!( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)
( 8,104)( 9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)
( 16,112)( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)
( 24,120)( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)
( 32,128)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)
( 40,136)( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)
( 48,144)( 49,148)( 50,149)( 51,150)( 52,145)( 53,146)( 54,147)( 55,154)
( 56,155)( 57,156)( 58,151)( 59,152)( 60,153)( 61,160)( 62,161)( 63,162)
( 64,157)( 65,158)( 66,159)( 67,166)( 68,167)( 69,168)( 70,163)( 71,164)
( 72,165)( 73,172)( 74,173)( 75,174)( 76,169)( 77,170)( 78,171)( 79,178)
( 80,179)( 81,180)( 82,175)( 83,176)( 84,177)( 85,184)( 86,185)( 87,186)
( 88,181)( 89,182)( 90,183)( 91,190)( 92,191)( 93,192)( 94,187)( 95,188)
( 96,189)(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)
(200,296)(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)
(208,304)(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)
(216,312)(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)
(224,320)(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)
(232,328)(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)
(240,336)(241,340)(242,341)(243,342)(244,337)(245,338)(246,339)(247,346)
(248,347)(249,348)(250,343)(251,344)(252,345)(253,352)(254,353)(255,354)
(256,349)(257,350)(258,351)(259,358)(260,359)(261,360)(262,355)(263,356)
(264,357)(265,364)(266,365)(267,366)(268,361)(269,362)(270,363)(271,370)
(272,371)(273,372)(274,367)(275,368)(276,369)(277,376)(278,377)(279,378)
(280,373)(281,374)(282,375)(283,382)(284,383)(285,384)(286,379)(287,380)
(288,381);
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*s2*s1*s2*s1*s0*s1*s0*s2*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s0*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