Polytope of Type {96,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {96,4}*768a
Also Known As : {96,4|2}. if this polytope has another name.
Group : SmallGroup(768,90209)
Rank : 3
Schlafli Type : {96,4}
Number of vertices, edges, etc : 96, 192, 4
Order of s0s1s2 : 96
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {48,4}*384a, {96,2}*384
3-fold quotients : {32,4}*256a
4-fold quotients : {24,4}*192a, {48,2}*192
6-fold quotients : {16,4}*128a, {32,2}*128
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)
( 25,217)( 26,219)( 27,218)( 28,220)( 29,222)( 30,221)( 31,226)( 32,228)
( 33,227)( 34,223)( 35,225)( 36,224)( 37,235)( 38,237)( 39,236)( 40,238)
( 41,240)( 42,239)( 43,229)( 44,231)( 45,230)( 46,232)( 47,234)( 48,233)
( 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)
( 73,277)( 74,279)( 75,278)( 76,280)( 77,282)( 78,281)( 79,286)( 80,288)
( 81,287)( 82,283)( 83,285)( 84,284)( 85,265)( 86,267)( 87,266)( 88,268)
( 89,270)( 90,269)( 91,274)( 92,276)( 93,275)( 94,271)( 95,273)( 96,272)
( 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)
(121,313)(122,315)(123,314)(124,316)(125,318)(126,317)(127,322)(128,324)
(129,323)(130,319)(131,321)(132,320)(133,331)(134,333)(135,332)(136,334)
(137,336)(138,335)(139,325)(140,327)(141,326)(142,328)(143,330)(144,329)
(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)
(169,373)(170,375)(171,374)(172,376)(173,378)(174,377)(175,382)(176,384)
(177,383)(178,379)(179,381)(180,380)(181,361)(182,363)(183,362)(184,364)
(185,366)(186,365)(187,370)(188,372)(189,371)(190,367)(191,369)(192,368);;
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)(289,363)(290,362)
(291,361)(292,366)(293,365)(294,364)(295,372)(296,371)(297,370)(298,369)
(299,368)(300,367)(301,381)(302,380)(303,379)(304,384)(305,383)(306,382)
(307,375)(308,374)(309,373)(310,378)(311,377)(312,376)(313,339)(314,338)
(315,337)(316,342)(317,341)(318,340)(319,348)(320,347)(321,346)(322,345)
(323,344)(324,343)(325,357)(326,356)(327,355)(328,360)(329,359)(330,358)
(331,351)(332,350)(333,349)(334,354)(335,353)(336,352);;
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)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)
( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,159)( 64,160)
( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)( 72,168)
( 73,169)( 74,170)( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)( 80,176)
( 81,177)( 82,178)( 83,179)( 84,180)( 85,181)( 86,182)( 87,183)( 88,184)
( 89,185)( 90,186)( 91,187)( 92,188)( 93,189)( 94,190)( 95,191)( 96,192)
(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)
(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)(248,344)
(249,345)(250,346)(251,347)(252,348)(253,349)(254,350)(255,351)(256,352)
(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)
(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)(272,368)
(273,369)(274,370)(275,371)(276,372)(277,373)(278,374)(279,375)(280,376)
(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)(288,384);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, 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*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*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*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)( 25,217)( 26,219)( 27,218)( 28,220)( 29,222)( 30,221)( 31,226)
( 32,228)( 33,227)( 34,223)( 35,225)( 36,224)( 37,235)( 38,237)( 39,236)
( 40,238)( 41,240)( 42,239)( 43,229)( 44,231)( 45,230)( 46,232)( 47,234)
( 48,233)( 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)( 73,277)( 74,279)( 75,278)( 76,280)( 77,282)( 78,281)( 79,286)
( 80,288)( 81,287)( 82,283)( 83,285)( 84,284)( 85,265)( 86,267)( 87,266)
( 88,268)( 89,270)( 90,269)( 91,274)( 92,276)( 93,275)( 94,271)( 95,273)
( 96,272)( 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)(121,313)(122,315)(123,314)(124,316)(125,318)(126,317)(127,322)
(128,324)(129,323)(130,319)(131,321)(132,320)(133,331)(134,333)(135,332)
(136,334)(137,336)(138,335)(139,325)(140,327)(141,326)(142,328)(143,330)
(144,329)(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)(169,373)(170,375)(171,374)(172,376)(173,378)(174,377)(175,382)
(176,384)(177,383)(178,379)(179,381)(180,380)(181,361)(182,363)(183,362)
(184,364)(185,366)(186,365)(187,370)(188,372)(189,371)(190,367)(191,369)
(192,368);
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)(289,363)
(290,362)(291,361)(292,366)(293,365)(294,364)(295,372)(296,371)(297,370)
(298,369)(299,368)(300,367)(301,381)(302,380)(303,379)(304,384)(305,383)
(306,382)(307,375)(308,374)(309,373)(310,378)(311,377)(312,376)(313,339)
(314,338)(315,337)(316,342)(317,341)(318,340)(319,348)(320,347)(321,346)
(322,345)(323,344)(324,343)(325,357)(326,356)(327,355)(328,360)(329,359)
(330,358)(331,351)(332,350)(333,349)(334,354)(335,353)(336,352);
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)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)
( 56,152)( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,159)
( 64,160)( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)
( 72,168)( 73,169)( 74,170)( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)
( 80,176)( 81,177)( 82,178)( 83,179)( 84,180)( 85,181)( 86,182)( 87,183)
( 88,184)( 89,185)( 90,186)( 91,187)( 92,188)( 93,189)( 94,190)( 95,191)
( 96,192)(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)(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)
(248,344)(249,345)(250,346)(251,347)(252,348)(253,349)(254,350)(255,351)
(256,352)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)
(264,360)(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)
(272,368)(273,369)(274,370)(275,371)(276,372)(277,373)(278,374)(279,375)
(280,376)(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)
(288,384);
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, 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*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*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*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