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# Polytope of Type {4,96}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,96}*768a
Also Known As : {4,96|2}. if this polytope has another name.
Group : SmallGroup(768,90209)
Rank : 3
Schlafli Type : {4,96}
Number of vertices, edges, etc : 4, 192, 96
Order of s0s1s2 : 96
Order of s0s1s2s1 : 2
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, {2,96}*384
3-fold quotients : {4,32}*256a
4-fold quotients : {4,24}*192a, {2,48}*192
6-fold quotients : {4,16}*128a, {2,32}*128
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)
( 49,145)( 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);;
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)(289,361)(290,363)
(291,362)(292,364)(293,366)(294,365)(295,370)(296,372)(297,371)(298,367)
(299,369)(300,368)(301,379)(302,381)(303,380)(304,382)(305,384)(306,383)
(307,373)(308,375)(309,374)(310,376)(311,378)(312,377)(313,337)(314,339)
(315,338)(316,340)(317,342)(318,341)(319,346)(320,348)(321,347)(322,343)
(323,345)(324,344)(325,355)(326,357)(327,356)(328,358)(329,360)(330,359)
(331,349)(332,351)(333,350)(334,352)(335,354)(336,353);;
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)
( 25,219)( 26,218)( 27,217)( 28,222)( 29,221)( 30,220)( 31,228)( 32,227)
( 33,226)( 34,225)( 35,224)( 36,223)( 37,237)( 38,236)( 39,235)( 40,240)
( 41,239)( 42,238)( 43,231)( 44,230)( 45,229)( 46,234)( 47,233)( 48,232)
( 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)
( 73,279)( 74,278)( 75,277)( 76,282)( 77,281)( 78,280)( 79,288)( 80,287)
( 81,286)( 82,285)( 83,284)( 84,283)( 85,267)( 86,266)( 87,265)( 88,270)
( 89,269)( 90,268)( 91,276)( 92,275)( 93,274)( 94,273)( 95,272)( 96,271)
( 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)
(121,315)(122,314)(123,313)(124,318)(125,317)(126,316)(127,324)(128,323)
(129,322)(130,321)(131,320)(132,319)(133,333)(134,332)(135,331)(136,336)
(137,335)(138,334)(139,327)(140,326)(141,325)(142,330)(143,329)(144,328)
(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)
(169,375)(170,374)(171,373)(172,378)(173,377)(174,376)(175,384)(176,383)
(177,382)(178,381)(179,380)(180,379)(181,363)(182,362)(183,361)(184,366)
(185,365)(186,364)(187,372)(188,371)(189,370)(190,369)(191,368)(192,367);;
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,
s0*s1*s2*s1*s0*s1*s2*s1, 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*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)( 49,145)( 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);
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)(289,361)
(290,363)(291,362)(292,364)(293,366)(294,365)(295,370)(296,372)(297,371)
(298,367)(299,369)(300,368)(301,379)(302,381)(303,380)(304,382)(305,384)
(306,383)(307,373)(308,375)(309,374)(310,376)(311,378)(312,377)(313,337)
(314,339)(315,338)(316,340)(317,342)(318,341)(319,346)(320,348)(321,347)
(322,343)(323,345)(324,344)(325,355)(326,357)(327,356)(328,358)(329,360)
(330,359)(331,349)(332,351)(333,350)(334,352)(335,354)(336,353);
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)( 25,219)( 26,218)( 27,217)( 28,222)( 29,221)( 30,220)( 31,228)
( 32,227)( 33,226)( 34,225)( 35,224)( 36,223)( 37,237)( 38,236)( 39,235)
( 40,240)( 41,239)( 42,238)( 43,231)( 44,230)( 45,229)( 46,234)( 47,233)
( 48,232)( 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)( 73,279)( 74,278)( 75,277)( 76,282)( 77,281)( 78,280)( 79,288)
( 80,287)( 81,286)( 82,285)( 83,284)( 84,283)( 85,267)( 86,266)( 87,265)
( 88,270)( 89,269)( 90,268)( 91,276)( 92,275)( 93,274)( 94,273)( 95,272)
( 96,271)( 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)(121,315)(122,314)(123,313)(124,318)(125,317)(126,316)(127,324)
(128,323)(129,322)(130,321)(131,320)(132,319)(133,333)(134,332)(135,331)
(136,336)(137,335)(138,334)(139,327)(140,326)(141,325)(142,330)(143,329)
(144,328)(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)(169,375)(170,374)(171,373)(172,378)(173,377)(174,376)(175,384)
(176,383)(177,382)(178,381)(179,380)(180,379)(181,363)(182,362)(183,361)
(184,366)(185,365)(186,364)(187,372)(188,371)(189,370)(190,369)(191,368)
(192,367);
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,
s0*s1*s2*s1*s0*s1*s2*s1, 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*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*s1*s2*s1*s2*s1*s2*s1*s2 >;

```
References : None.
to this polytope