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# Polytope of Type {96,4}

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