Polytope of Type {96,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {96,4}*768d
if this polytope has a name.
Group : SmallGroup(768,1086056)
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
Non-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}*384c
4-fold quotients : {24,4}*192c
8-fold quotients : {12,4}*96b
16-fold quotients : {6,4}*48c
32-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)
( 19, 24)( 20, 23)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)( 30, 46)
( 31, 48)( 32, 47)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 49, 73)( 50, 74)
( 51, 76)( 52, 75)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 57, 77)( 58, 78)
( 59, 80)( 60, 79)( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 65, 93)( 66, 94)
( 67, 96)( 68, 95)( 69, 89)( 70, 90)( 71, 92)( 72, 91)( 97,145)( 98,146)
( 99,148)(100,147)(101,153)(102,154)(103,156)(104,155)(105,149)(106,150)
(107,152)(108,151)(109,157)(110,158)(111,160)(112,159)(113,165)(114,166)
(115,168)(116,167)(117,161)(118,162)(119,164)(120,163)(121,181)(122,182)
(123,184)(124,183)(125,189)(126,190)(127,192)(128,191)(129,185)(130,186)
(131,188)(132,187)(133,169)(134,170)(135,172)(136,171)(137,177)(138,178)
(139,180)(140,179)(141,173)(142,174)(143,176)(144,175)(193,289)(194,290)
(195,292)(196,291)(197,297)(198,298)(199,300)(200,299)(201,293)(202,294)
(203,296)(204,295)(205,301)(206,302)(207,304)(208,303)(209,309)(210,310)
(211,312)(212,311)(213,305)(214,306)(215,308)(216,307)(217,325)(218,326)
(219,328)(220,327)(221,333)(222,334)(223,336)(224,335)(225,329)(226,330)
(227,332)(228,331)(229,313)(230,314)(231,316)(232,315)(233,321)(234,322)
(235,324)(236,323)(237,317)(238,318)(239,320)(240,319)(241,361)(242,362)
(243,364)(244,363)(245,369)(246,370)(247,372)(248,371)(249,365)(250,366)
(251,368)(252,367)(253,373)(254,374)(255,376)(256,375)(257,381)(258,382)
(259,384)(260,383)(261,377)(262,378)(263,380)(264,379)(265,337)(266,338)
(267,340)(268,339)(269,345)(270,346)(271,348)(272,347)(273,341)(274,342)
(275,344)(276,343)(277,349)(278,350)(279,352)(280,351)(281,357)(282,358)
(283,360)(284,359)(285,353)(286,354)(287,356)(288,355);;
s1 := ( 1,297)( 2,299)( 3,298)( 4,300)( 5,293)( 6,295)( 7,294)( 8,296)
( 9,289)( 10,291)( 11,290)( 12,292)( 13,309)( 14,311)( 15,310)( 16,312)
( 17,305)( 18,307)( 19,306)( 20,308)( 21,301)( 22,303)( 23,302)( 24,304)
( 25,333)( 26,335)( 27,334)( 28,336)( 29,329)( 30,331)( 31,330)( 32,332)
( 33,325)( 34,327)( 35,326)( 36,328)( 37,321)( 38,323)( 39,322)( 40,324)
( 41,317)( 42,319)( 43,318)( 44,320)( 45,313)( 46,315)( 47,314)( 48,316)
( 49,369)( 50,371)( 51,370)( 52,372)( 53,365)( 54,367)( 55,366)( 56,368)
( 57,361)( 58,363)( 59,362)( 60,364)( 61,381)( 62,383)( 63,382)( 64,384)
( 65,377)( 66,379)( 67,378)( 68,380)( 69,373)( 70,375)( 71,374)( 72,376)
( 73,345)( 74,347)( 75,346)( 76,348)( 77,341)( 78,343)( 79,342)( 80,344)
( 81,337)( 82,339)( 83,338)( 84,340)( 85,357)( 86,359)( 87,358)( 88,360)
( 89,353)( 90,355)( 91,354)( 92,356)( 93,349)( 94,351)( 95,350)( 96,352)
( 97,201)( 98,203)( 99,202)(100,204)(101,197)(102,199)(103,198)(104,200)
(105,193)(106,195)(107,194)(108,196)(109,213)(110,215)(111,214)(112,216)
(113,209)(114,211)(115,210)(116,212)(117,205)(118,207)(119,206)(120,208)
(121,237)(122,239)(123,238)(124,240)(125,233)(126,235)(127,234)(128,236)
(129,229)(130,231)(131,230)(132,232)(133,225)(134,227)(135,226)(136,228)
(137,221)(138,223)(139,222)(140,224)(141,217)(142,219)(143,218)(144,220)
(145,273)(146,275)(147,274)(148,276)(149,269)(150,271)(151,270)(152,272)
(153,265)(154,267)(155,266)(156,268)(157,285)(158,287)(159,286)(160,288)
(161,281)(162,283)(163,282)(164,284)(165,277)(166,279)(167,278)(168,280)
(169,249)(170,251)(171,250)(172,252)(173,245)(174,247)(175,246)(176,248)
(177,241)(178,243)(179,242)(180,244)(181,261)(182,263)(183,262)(184,264)
(185,257)(186,259)(187,258)(188,260)(189,253)(190,255)(191,254)(192,256);;
s2 := ( 1, 14)( 2, 13)( 3, 16)( 4, 15)( 5, 18)( 6, 17)( 7, 20)( 8, 19)
( 9, 22)( 10, 21)( 11, 24)( 12, 23)( 25, 38)( 26, 37)( 27, 40)( 28, 39)
( 29, 42)( 30, 41)( 31, 44)( 32, 43)( 33, 46)( 34, 45)( 35, 48)( 36, 47)
( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 66)( 54, 65)( 55, 68)( 56, 67)
( 57, 70)( 58, 69)( 59, 72)( 60, 71)( 73, 86)( 74, 85)( 75, 88)( 76, 87)
( 77, 90)( 78, 89)( 79, 92)( 80, 91)( 81, 94)( 82, 93)( 83, 96)( 84, 95)
( 97,110)( 98,109)( 99,112)(100,111)(101,114)(102,113)(103,116)(104,115)
(105,118)(106,117)(107,120)(108,119)(121,134)(122,133)(123,136)(124,135)
(125,138)(126,137)(127,140)(128,139)(129,142)(130,141)(131,144)(132,143)
(145,158)(146,157)(147,160)(148,159)(149,162)(150,161)(151,164)(152,163)
(153,166)(154,165)(155,168)(156,167)(169,182)(170,181)(171,184)(172,183)
(173,186)(174,185)(175,188)(176,187)(177,190)(178,189)(179,192)(180,191)
(193,206)(194,205)(195,208)(196,207)(197,210)(198,209)(199,212)(200,211)
(201,214)(202,213)(203,216)(204,215)(217,230)(218,229)(219,232)(220,231)
(221,234)(222,233)(223,236)(224,235)(225,238)(226,237)(227,240)(228,239)
(241,254)(242,253)(243,256)(244,255)(245,258)(246,257)(247,260)(248,259)
(249,262)(250,261)(251,264)(252,263)(265,278)(266,277)(267,280)(268,279)
(269,282)(270,281)(271,284)(272,283)(273,286)(274,285)(275,288)(276,287)
(289,302)(290,301)(291,304)(292,303)(293,306)(294,305)(295,308)(296,307)
(297,310)(298,309)(299,312)(300,311)(313,326)(314,325)(315,328)(316,327)
(317,330)(318,329)(319,332)(320,331)(321,334)(322,333)(323,336)(324,335)
(337,350)(338,349)(339,352)(340,351)(341,354)(342,353)(343,356)(344,355)
(345,358)(346,357)(347,360)(348,359)(361,374)(362,373)(363,376)(364,375)
(365,378)(366,377)(367,380)(368,379)(369,382)(370,381)(371,384)(372,383);;
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*s2*s1*s0*s1*s0*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*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*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)
( 18, 22)( 19, 24)( 20, 23)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)
( 30, 46)( 31, 48)( 32, 47)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 49, 73)
( 50, 74)( 51, 76)( 52, 75)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 57, 77)
( 58, 78)( 59, 80)( 60, 79)( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 65, 93)
( 66, 94)( 67, 96)( 68, 95)( 69, 89)( 70, 90)( 71, 92)( 72, 91)( 97,145)
( 98,146)( 99,148)(100,147)(101,153)(102,154)(103,156)(104,155)(105,149)
(106,150)(107,152)(108,151)(109,157)(110,158)(111,160)(112,159)(113,165)
(114,166)(115,168)(116,167)(117,161)(118,162)(119,164)(120,163)(121,181)
(122,182)(123,184)(124,183)(125,189)(126,190)(127,192)(128,191)(129,185)
(130,186)(131,188)(132,187)(133,169)(134,170)(135,172)(136,171)(137,177)
(138,178)(139,180)(140,179)(141,173)(142,174)(143,176)(144,175)(193,289)
(194,290)(195,292)(196,291)(197,297)(198,298)(199,300)(200,299)(201,293)
(202,294)(203,296)(204,295)(205,301)(206,302)(207,304)(208,303)(209,309)
(210,310)(211,312)(212,311)(213,305)(214,306)(215,308)(216,307)(217,325)
(218,326)(219,328)(220,327)(221,333)(222,334)(223,336)(224,335)(225,329)
(226,330)(227,332)(228,331)(229,313)(230,314)(231,316)(232,315)(233,321)
(234,322)(235,324)(236,323)(237,317)(238,318)(239,320)(240,319)(241,361)
(242,362)(243,364)(244,363)(245,369)(246,370)(247,372)(248,371)(249,365)
(250,366)(251,368)(252,367)(253,373)(254,374)(255,376)(256,375)(257,381)
(258,382)(259,384)(260,383)(261,377)(262,378)(263,380)(264,379)(265,337)
(266,338)(267,340)(268,339)(269,345)(270,346)(271,348)(272,347)(273,341)
(274,342)(275,344)(276,343)(277,349)(278,350)(279,352)(280,351)(281,357)
(282,358)(283,360)(284,359)(285,353)(286,354)(287,356)(288,355);
s1 := Sym(384)!( 1,297)( 2,299)( 3,298)( 4,300)( 5,293)( 6,295)( 7,294)
( 8,296)( 9,289)( 10,291)( 11,290)( 12,292)( 13,309)( 14,311)( 15,310)
( 16,312)( 17,305)( 18,307)( 19,306)( 20,308)( 21,301)( 22,303)( 23,302)
( 24,304)( 25,333)( 26,335)( 27,334)( 28,336)( 29,329)( 30,331)( 31,330)
( 32,332)( 33,325)( 34,327)( 35,326)( 36,328)( 37,321)( 38,323)( 39,322)
( 40,324)( 41,317)( 42,319)( 43,318)( 44,320)( 45,313)( 46,315)( 47,314)
( 48,316)( 49,369)( 50,371)( 51,370)( 52,372)( 53,365)( 54,367)( 55,366)
( 56,368)( 57,361)( 58,363)( 59,362)( 60,364)( 61,381)( 62,383)( 63,382)
( 64,384)( 65,377)( 66,379)( 67,378)( 68,380)( 69,373)( 70,375)( 71,374)
( 72,376)( 73,345)( 74,347)( 75,346)( 76,348)( 77,341)( 78,343)( 79,342)
( 80,344)( 81,337)( 82,339)( 83,338)( 84,340)( 85,357)( 86,359)( 87,358)
( 88,360)( 89,353)( 90,355)( 91,354)( 92,356)( 93,349)( 94,351)( 95,350)
( 96,352)( 97,201)( 98,203)( 99,202)(100,204)(101,197)(102,199)(103,198)
(104,200)(105,193)(106,195)(107,194)(108,196)(109,213)(110,215)(111,214)
(112,216)(113,209)(114,211)(115,210)(116,212)(117,205)(118,207)(119,206)
(120,208)(121,237)(122,239)(123,238)(124,240)(125,233)(126,235)(127,234)
(128,236)(129,229)(130,231)(131,230)(132,232)(133,225)(134,227)(135,226)
(136,228)(137,221)(138,223)(139,222)(140,224)(141,217)(142,219)(143,218)
(144,220)(145,273)(146,275)(147,274)(148,276)(149,269)(150,271)(151,270)
(152,272)(153,265)(154,267)(155,266)(156,268)(157,285)(158,287)(159,286)
(160,288)(161,281)(162,283)(163,282)(164,284)(165,277)(166,279)(167,278)
(168,280)(169,249)(170,251)(171,250)(172,252)(173,245)(174,247)(175,246)
(176,248)(177,241)(178,243)(179,242)(180,244)(181,261)(182,263)(183,262)
(184,264)(185,257)(186,259)(187,258)(188,260)(189,253)(190,255)(191,254)
(192,256);
s2 := Sym(384)!( 1, 14)( 2, 13)( 3, 16)( 4, 15)( 5, 18)( 6, 17)( 7, 20)
( 8, 19)( 9, 22)( 10, 21)( 11, 24)( 12, 23)( 25, 38)( 26, 37)( 27, 40)
( 28, 39)( 29, 42)( 30, 41)( 31, 44)( 32, 43)( 33, 46)( 34, 45)( 35, 48)
( 36, 47)( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 66)( 54, 65)( 55, 68)
( 56, 67)( 57, 70)( 58, 69)( 59, 72)( 60, 71)( 73, 86)( 74, 85)( 75, 88)
( 76, 87)( 77, 90)( 78, 89)( 79, 92)( 80, 91)( 81, 94)( 82, 93)( 83, 96)
( 84, 95)( 97,110)( 98,109)( 99,112)(100,111)(101,114)(102,113)(103,116)
(104,115)(105,118)(106,117)(107,120)(108,119)(121,134)(122,133)(123,136)
(124,135)(125,138)(126,137)(127,140)(128,139)(129,142)(130,141)(131,144)
(132,143)(145,158)(146,157)(147,160)(148,159)(149,162)(150,161)(151,164)
(152,163)(153,166)(154,165)(155,168)(156,167)(169,182)(170,181)(171,184)
(172,183)(173,186)(174,185)(175,188)(176,187)(177,190)(178,189)(179,192)
(180,191)(193,206)(194,205)(195,208)(196,207)(197,210)(198,209)(199,212)
(200,211)(201,214)(202,213)(203,216)(204,215)(217,230)(218,229)(219,232)
(220,231)(221,234)(222,233)(223,236)(224,235)(225,238)(226,237)(227,240)
(228,239)(241,254)(242,253)(243,256)(244,255)(245,258)(246,257)(247,260)
(248,259)(249,262)(250,261)(251,264)(252,263)(265,278)(266,277)(267,280)
(268,279)(269,282)(270,281)(271,284)(272,283)(273,286)(274,285)(275,288)
(276,287)(289,302)(290,301)(291,304)(292,303)(293,306)(294,305)(295,308)
(296,307)(297,310)(298,309)(299,312)(300,311)(313,326)(314,325)(315,328)
(316,327)(317,330)(318,329)(319,332)(320,331)(321,334)(322,333)(323,336)
(324,335)(337,350)(338,349)(339,352)(340,351)(341,354)(342,353)(343,356)
(344,355)(345,358)(346,357)(347,360)(348,359)(361,374)(362,373)(363,376)
(364,375)(365,378)(366,377)(367,380)(368,379)(369,382)(370,381)(371,384)
(372,383);
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*s2*s1*s0*s1*s0*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*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*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope