Polytope of Type {4,96}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,96}*768b
if this polytope has a name.
Group : SmallGroup(768,90243)
Rank : 3
Schlafli Type : {4,96}
Number of vertices, edges, etc : 4, 192, 96
Order of s0s1s2 : 96
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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) :
2-fold quotients : {4,48}*384a
3-fold quotients : {4,32}*256b
4-fold quotients : {4,24}*192a, {2,48}*192
6-fold quotients : {4,16}*128a
8-fold quotients : {4,12}*96a, {2,24}*96
12-fold quotients : {4,8}*64a, {2,16}*64
16-fold quotients : {2,12}*48, {4,6}*48a
24-fold quotients : {4,4}*32, {2,8}*32
32-fold quotients : {2,6}*24
48-fold quotients : {2,4}*16, {4,2}*16
64-fold quotients : {2,3}*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)( 5,101)( 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);;
s1 := ( 2, 3)( 5, 6)( 7, 10)( 8, 12)( 9, 11)( 13, 19)( 14, 21)( 15, 20)
( 16, 22)( 17, 24)( 18, 23)( 26, 27)( 29, 30)( 31, 34)( 32, 36)( 33, 35)
( 37, 43)( 38, 45)( 39, 44)( 40, 46)( 41, 48)( 42, 47)( 49, 61)( 50, 63)
( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)( 58, 67)
( 59, 69)( 60, 68)( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)( 78, 89)
( 79, 94)( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)( 98,123)
( 99,122)(100,124)(101,126)(102,125)(103,130)(104,132)(105,131)(106,127)
(107,129)(108,128)(109,139)(110,141)(111,140)(112,142)(113,144)(114,143)
(115,133)(116,135)(117,134)(118,136)(119,138)(120,137)(145,181)(146,183)
(147,182)(148,184)(149,186)(150,185)(151,190)(152,192)(153,191)(154,187)
(155,189)(156,188)(157,169)(158,171)(159,170)(160,172)(161,174)(162,173)
(163,178)(164,180)(165,179)(166,175)(167,177)(168,176)(193,241)(194,243)
(195,242)(196,244)(197,246)(198,245)(199,250)(200,252)(201,251)(202,247)
(203,249)(204,248)(205,259)(206,261)(207,260)(208,262)(209,264)(210,263)
(211,253)(212,255)(213,254)(214,256)(215,258)(216,257)(217,265)(218,267)
(219,266)(220,268)(221,270)(222,269)(223,274)(224,276)(225,275)(226,271)
(227,273)(228,272)(229,283)(230,285)(231,284)(232,286)(233,288)(234,287)
(235,277)(236,279)(237,278)(238,280)(239,282)(240,281)(289,364)(290,366)
(291,365)(292,361)(293,363)(294,362)(295,367)(296,369)(297,368)(298,370)
(299,372)(300,371)(301,382)(302,384)(303,383)(304,379)(305,381)(306,380)
(307,376)(308,378)(309,377)(310,373)(311,375)(312,374)(313,340)(314,342)
(315,341)(316,337)(317,339)(318,338)(319,343)(320,345)(321,344)(322,346)
(323,348)(324,347)(325,358)(326,360)(327,359)(328,355)(329,357)(330,356)
(331,352)(332,354)(333,353)(334,349)(335,351)(336,350);;
s2 := ( 1,195)( 2,194)( 3,193)( 4,198)( 5,197)( 6,196)( 7,204)( 8,203)
( 9,202)( 10,201)( 11,200)( 12,199)( 13,213)( 14,212)( 15,211)( 16,216)
( 17,215)( 18,214)( 19,207)( 20,206)( 21,205)( 22,210)( 23,209)( 24,208)
( 25,222)( 26,221)( 27,220)( 28,219)( 29,218)( 30,217)( 31,225)( 32,224)
( 33,223)( 34,228)( 35,227)( 36,226)( 37,240)( 38,239)( 39,238)( 40,237)
( 41,236)( 42,235)( 43,234)( 44,233)( 45,232)( 46,231)( 47,230)( 48,229)
( 49,255)( 50,254)( 51,253)( 52,258)( 53,257)( 54,256)( 55,264)( 56,263)
( 57,262)( 58,261)( 59,260)( 60,259)( 61,243)( 62,242)( 63,241)( 64,246)
( 65,245)( 66,244)( 67,252)( 68,251)( 69,250)( 70,249)( 71,248)( 72,247)
( 73,282)( 74,281)( 75,280)( 76,279)( 77,278)( 78,277)( 79,285)( 80,284)
( 81,283)( 82,288)( 83,287)( 84,286)( 85,270)( 86,269)( 87,268)( 88,267)
( 89,266)( 90,265)( 91,273)( 92,272)( 93,271)( 94,276)( 95,275)( 96,274)
( 97,291)( 98,290)( 99,289)(100,294)(101,293)(102,292)(103,300)(104,299)
(105,298)(106,297)(107,296)(108,295)(109,309)(110,308)(111,307)(112,312)
(113,311)(114,310)(115,303)(116,302)(117,301)(118,306)(119,305)(120,304)
(121,318)(122,317)(123,316)(124,315)(125,314)(126,313)(127,321)(128,320)
(129,319)(130,324)(131,323)(132,322)(133,336)(134,335)(135,334)(136,333)
(137,332)(138,331)(139,330)(140,329)(141,328)(142,327)(143,326)(144,325)
(145,351)(146,350)(147,349)(148,354)(149,353)(150,352)(151,360)(152,359)
(153,358)(154,357)(155,356)(156,355)(157,339)(158,338)(159,337)(160,342)
(161,341)(162,340)(163,348)(164,347)(165,346)(166,345)(167,344)(168,343)
(169,378)(170,377)(171,376)(172,375)(173,374)(174,373)(175,381)(176,380)
(177,379)(178,384)(179,383)(180,382)(181,366)(182,365)(183,364)(184,363)
(185,362)(186,361)(187,369)(188,368)(189,367)(190,372)(191,371)(192,370);;
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,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*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*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(384)!( 2, 3)( 5, 6)( 7, 10)( 8, 12)( 9, 11)( 13, 19)( 14, 21)
( 15, 20)( 16, 22)( 17, 24)( 18, 23)( 26, 27)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 43)( 38, 45)( 39, 44)( 40, 46)( 41, 48)( 42, 47)( 49, 61)
( 50, 63)( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)
( 58, 67)( 59, 69)( 60, 68)( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)
( 78, 89)( 79, 94)( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)
( 98,123)( 99,122)(100,124)(101,126)(102,125)(103,130)(104,132)(105,131)
(106,127)(107,129)(108,128)(109,139)(110,141)(111,140)(112,142)(113,144)
(114,143)(115,133)(116,135)(117,134)(118,136)(119,138)(120,137)(145,181)
(146,183)(147,182)(148,184)(149,186)(150,185)(151,190)(152,192)(153,191)
(154,187)(155,189)(156,188)(157,169)(158,171)(159,170)(160,172)(161,174)
(162,173)(163,178)(164,180)(165,179)(166,175)(167,177)(168,176)(193,241)
(194,243)(195,242)(196,244)(197,246)(198,245)(199,250)(200,252)(201,251)
(202,247)(203,249)(204,248)(205,259)(206,261)(207,260)(208,262)(209,264)
(210,263)(211,253)(212,255)(213,254)(214,256)(215,258)(216,257)(217,265)
(218,267)(219,266)(220,268)(221,270)(222,269)(223,274)(224,276)(225,275)
(226,271)(227,273)(228,272)(229,283)(230,285)(231,284)(232,286)(233,288)
(234,287)(235,277)(236,279)(237,278)(238,280)(239,282)(240,281)(289,364)
(290,366)(291,365)(292,361)(293,363)(294,362)(295,367)(296,369)(297,368)
(298,370)(299,372)(300,371)(301,382)(302,384)(303,383)(304,379)(305,381)
(306,380)(307,376)(308,378)(309,377)(310,373)(311,375)(312,374)(313,340)
(314,342)(315,341)(316,337)(317,339)(318,338)(319,343)(320,345)(321,344)
(322,346)(323,348)(324,347)(325,358)(326,360)(327,359)(328,355)(329,357)
(330,356)(331,352)(332,354)(333,353)(334,349)(335,351)(336,350);
s2 := Sym(384)!( 1,195)( 2,194)( 3,193)( 4,198)( 5,197)( 6,196)( 7,204)
( 8,203)( 9,202)( 10,201)( 11,200)( 12,199)( 13,213)( 14,212)( 15,211)
( 16,216)( 17,215)( 18,214)( 19,207)( 20,206)( 21,205)( 22,210)( 23,209)
( 24,208)( 25,222)( 26,221)( 27,220)( 28,219)( 29,218)( 30,217)( 31,225)
( 32,224)( 33,223)( 34,228)( 35,227)( 36,226)( 37,240)( 38,239)( 39,238)
( 40,237)( 41,236)( 42,235)( 43,234)( 44,233)( 45,232)( 46,231)( 47,230)
( 48,229)( 49,255)( 50,254)( 51,253)( 52,258)( 53,257)( 54,256)( 55,264)
( 56,263)( 57,262)( 58,261)( 59,260)( 60,259)( 61,243)( 62,242)( 63,241)
( 64,246)( 65,245)( 66,244)( 67,252)( 68,251)( 69,250)( 70,249)( 71,248)
( 72,247)( 73,282)( 74,281)( 75,280)( 76,279)( 77,278)( 78,277)( 79,285)
( 80,284)( 81,283)( 82,288)( 83,287)( 84,286)( 85,270)( 86,269)( 87,268)
( 88,267)( 89,266)( 90,265)( 91,273)( 92,272)( 93,271)( 94,276)( 95,275)
( 96,274)( 97,291)( 98,290)( 99,289)(100,294)(101,293)(102,292)(103,300)
(104,299)(105,298)(106,297)(107,296)(108,295)(109,309)(110,308)(111,307)
(112,312)(113,311)(114,310)(115,303)(116,302)(117,301)(118,306)(119,305)
(120,304)(121,318)(122,317)(123,316)(124,315)(125,314)(126,313)(127,321)
(128,320)(129,319)(130,324)(131,323)(132,322)(133,336)(134,335)(135,334)
(136,333)(137,332)(138,331)(139,330)(140,329)(141,328)(142,327)(143,326)
(144,325)(145,351)(146,350)(147,349)(148,354)(149,353)(150,352)(151,360)
(152,359)(153,358)(154,357)(155,356)(156,355)(157,339)(158,338)(159,337)
(160,342)(161,341)(162,340)(163,348)(164,347)(165,346)(166,345)(167,344)
(168,343)(169,378)(170,377)(171,376)(172,375)(173,374)(174,373)(175,381)
(176,380)(177,379)(178,384)(179,383)(180,382)(181,366)(182,365)(183,364)
(184,363)(185,362)(186,361)(187,369)(188,368)(189,367)(190,372)(191,371)
(192,370);
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*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*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*s0*s1*s2*s1 >;
References : None.
to this polytope