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# Polytope of Type {4,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,48}*768c
if this polytope has a name.
Group : SmallGroup(768,1088569)
Rank : 3
Schlafli Type : {4,48}
Number of vertices, edges, etc : 8, 192, 96
Order of s0s1s2 : 48
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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}*384c, {4,48}*384d, {4,24}*384c
4-fold quotients : {2,48}*192, {4,24}*192c, {4,24}*192d, {4,12}*192b
8-fold quotients : {2,24}*96, {4,12}*96b, {4,12}*96c, {4,6}*96
12-fold quotients : {2,16}*64
16-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
24-fold quotients : {2,8}*32
32-fold quotients : {4,3}*24, {2,6}*24
48-fold quotients : {2,4}*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 := (  1,196)(  2,195)(  3,194)(  4,193)(  5,200)(  6,199)(  7,198)(  8,197)
(  9,204)( 10,203)( 11,202)( 12,201)( 13,208)( 14,207)( 15,206)( 16,205)
( 17,212)( 18,211)( 19,210)( 20,209)( 21,216)( 22,215)( 23,214)( 24,213)
( 25,220)( 26,219)( 27,218)( 28,217)( 29,224)( 30,223)( 31,222)( 32,221)
( 33,228)( 34,227)( 35,226)( 36,225)( 37,232)( 38,231)( 39,230)( 40,229)
( 41,236)( 42,235)( 43,234)( 44,233)( 45,240)( 46,239)( 47,238)( 48,237)
( 49,244)( 50,243)( 51,242)( 52,241)( 53,248)( 54,247)( 55,246)( 56,245)
( 57,252)( 58,251)( 59,250)( 60,249)( 61,256)( 62,255)( 63,254)( 64,253)
( 65,260)( 66,259)( 67,258)( 68,257)( 69,264)( 70,263)( 71,262)( 72,261)
( 73,268)( 74,267)( 75,266)( 76,265)( 77,272)( 78,271)( 79,270)( 80,269)
( 81,276)( 82,275)( 83,274)( 84,273)( 85,280)( 86,279)( 87,278)( 88,277)
( 89,284)( 90,283)( 91,282)( 92,281)( 93,288)( 94,287)( 95,286)( 96,285)
( 97,292)( 98,291)( 99,290)(100,289)(101,296)(102,295)(103,294)(104,293)
(105,300)(106,299)(107,298)(108,297)(109,304)(110,303)(111,302)(112,301)
(113,308)(114,307)(115,306)(116,305)(117,312)(118,311)(119,310)(120,309)
(121,316)(122,315)(123,314)(124,313)(125,320)(126,319)(127,318)(128,317)
(129,324)(130,323)(131,322)(132,321)(133,328)(134,327)(135,326)(136,325)
(137,332)(138,331)(139,330)(140,329)(141,336)(142,335)(143,334)(144,333)
(145,340)(146,339)(147,338)(148,337)(149,344)(150,343)(151,342)(152,341)
(153,348)(154,347)(155,346)(156,345)(157,352)(158,351)(159,350)(160,349)
(161,356)(162,355)(163,354)(164,353)(165,360)(166,359)(167,358)(168,357)
(169,364)(170,363)(171,362)(172,361)(173,368)(174,367)(175,366)(176,365)
(177,372)(178,371)(179,370)(180,369)(181,376)(182,375)(183,374)(184,373)
(185,380)(186,379)(187,378)(188,377)(189,384)(190,383)(191,382)(192,381);;
s1 := (  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)(195,196)(197,201)
(198,202)(199,204)(200,203)(207,208)(209,213)(210,214)(211,216)(212,215)
(217,229)(218,230)(219,232)(220,231)(221,237)(222,238)(223,240)(224,239)
(225,233)(226,234)(227,236)(228,235)(241,265)(242,266)(243,268)(244,267)
(245,273)(246,274)(247,276)(248,275)(249,269)(250,270)(251,272)(252,271)
(253,277)(254,278)(255,280)(256,279)(257,285)(258,286)(259,288)(260,287)
(261,281)(262,282)(263,284)(264,283)(289,337)(290,338)(291,340)(292,339)
(293,345)(294,346)(295,348)(296,347)(297,341)(298,342)(299,344)(300,343)
(301,349)(302,350)(303,352)(304,351)(305,357)(306,358)(307,360)(308,359)
(309,353)(310,354)(311,356)(312,355)(313,373)(314,374)(315,376)(316,375)
(317,381)(318,382)(319,384)(320,383)(321,377)(322,378)(323,380)(324,379)
(325,361)(326,362)(327,364)(328,363)(329,369)(330,370)(331,372)(332,371)
(333,365)(334,366)(335,368)(336,367);;
s2 := (  1,153)(  2,155)(  3,154)(  4,156)(  5,149)(  6,151)(  7,150)(  8,152)
(  9,145)( 10,147)( 11,146)( 12,148)( 13,165)( 14,167)( 15,166)( 16,168)
( 17,161)( 18,163)( 19,162)( 20,164)( 21,157)( 22,159)( 23,158)( 24,160)
( 25,189)( 26,191)( 27,190)( 28,192)( 29,185)( 30,187)( 31,186)( 32,188)
( 33,181)( 34,183)( 35,182)( 36,184)( 37,177)( 38,179)( 39,178)( 40,180)
( 41,173)( 42,175)( 43,174)( 44,176)( 45,169)( 46,171)( 47,170)( 48,172)
( 49,105)( 50,107)( 51,106)( 52,108)( 53,101)( 54,103)( 55,102)( 56,104)
( 57, 97)( 58, 99)( 59, 98)( 60,100)( 61,117)( 62,119)( 63,118)( 64,120)
( 65,113)( 66,115)( 67,114)( 68,116)( 69,109)( 70,111)( 71,110)( 72,112)
( 73,141)( 74,143)( 75,142)( 76,144)( 77,137)( 78,139)( 79,138)( 80,140)
( 81,133)( 82,135)( 83,134)( 84,136)( 85,129)( 86,131)( 87,130)( 88,132)
( 89,125)( 90,127)( 91,126)( 92,128)( 93,121)( 94,123)( 95,122)( 96,124)
(193,345)(194,347)(195,346)(196,348)(197,341)(198,343)(199,342)(200,344)
(201,337)(202,339)(203,338)(204,340)(205,357)(206,359)(207,358)(208,360)
(209,353)(210,355)(211,354)(212,356)(213,349)(214,351)(215,350)(216,352)
(217,381)(218,383)(219,382)(220,384)(221,377)(222,379)(223,378)(224,380)
(225,373)(226,375)(227,374)(228,376)(229,369)(230,371)(231,370)(232,372)
(233,365)(234,367)(235,366)(236,368)(237,361)(238,363)(239,362)(240,364)
(241,297)(242,299)(243,298)(244,300)(245,293)(246,295)(247,294)(248,296)
(249,289)(250,291)(251,290)(252,292)(253,309)(254,311)(255,310)(256,312)
(257,305)(258,307)(259,306)(260,308)(261,301)(262,303)(263,302)(264,304)
(265,333)(266,335)(267,334)(268,336)(269,329)(270,331)(271,330)(272,332)
(273,325)(274,327)(275,326)(276,328)(277,321)(278,323)(279,322)(280,324)
(281,317)(282,319)(283,318)(284,320)(285,313)(286,315)(287,314)(288,316);;
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*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(384)!(  1,196)(  2,195)(  3,194)(  4,193)(  5,200)(  6,199)(  7,198)
(  8,197)(  9,204)( 10,203)( 11,202)( 12,201)( 13,208)( 14,207)( 15,206)
( 16,205)( 17,212)( 18,211)( 19,210)( 20,209)( 21,216)( 22,215)( 23,214)
( 24,213)( 25,220)( 26,219)( 27,218)( 28,217)( 29,224)( 30,223)( 31,222)
( 32,221)( 33,228)( 34,227)( 35,226)( 36,225)( 37,232)( 38,231)( 39,230)
( 40,229)( 41,236)( 42,235)( 43,234)( 44,233)( 45,240)( 46,239)( 47,238)
( 48,237)( 49,244)( 50,243)( 51,242)( 52,241)( 53,248)( 54,247)( 55,246)
( 56,245)( 57,252)( 58,251)( 59,250)( 60,249)( 61,256)( 62,255)( 63,254)
( 64,253)( 65,260)( 66,259)( 67,258)( 68,257)( 69,264)( 70,263)( 71,262)
( 72,261)( 73,268)( 74,267)( 75,266)( 76,265)( 77,272)( 78,271)( 79,270)
( 80,269)( 81,276)( 82,275)( 83,274)( 84,273)( 85,280)( 86,279)( 87,278)
( 88,277)( 89,284)( 90,283)( 91,282)( 92,281)( 93,288)( 94,287)( 95,286)
( 96,285)( 97,292)( 98,291)( 99,290)(100,289)(101,296)(102,295)(103,294)
(104,293)(105,300)(106,299)(107,298)(108,297)(109,304)(110,303)(111,302)
(112,301)(113,308)(114,307)(115,306)(116,305)(117,312)(118,311)(119,310)
(120,309)(121,316)(122,315)(123,314)(124,313)(125,320)(126,319)(127,318)
(128,317)(129,324)(130,323)(131,322)(132,321)(133,328)(134,327)(135,326)
(136,325)(137,332)(138,331)(139,330)(140,329)(141,336)(142,335)(143,334)
(144,333)(145,340)(146,339)(147,338)(148,337)(149,344)(150,343)(151,342)
(152,341)(153,348)(154,347)(155,346)(156,345)(157,352)(158,351)(159,350)
(160,349)(161,356)(162,355)(163,354)(164,353)(165,360)(166,359)(167,358)
(168,357)(169,364)(170,363)(171,362)(172,361)(173,368)(174,367)(175,366)
(176,365)(177,372)(178,371)(179,370)(180,369)(181,376)(182,375)(183,374)
(184,373)(185,380)(186,379)(187,378)(188,377)(189,384)(190,383)(191,382)
(192,381);
s1 := 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)(195,196)
(197,201)(198,202)(199,204)(200,203)(207,208)(209,213)(210,214)(211,216)
(212,215)(217,229)(218,230)(219,232)(220,231)(221,237)(222,238)(223,240)
(224,239)(225,233)(226,234)(227,236)(228,235)(241,265)(242,266)(243,268)
(244,267)(245,273)(246,274)(247,276)(248,275)(249,269)(250,270)(251,272)
(252,271)(253,277)(254,278)(255,280)(256,279)(257,285)(258,286)(259,288)
(260,287)(261,281)(262,282)(263,284)(264,283)(289,337)(290,338)(291,340)
(292,339)(293,345)(294,346)(295,348)(296,347)(297,341)(298,342)(299,344)
(300,343)(301,349)(302,350)(303,352)(304,351)(305,357)(306,358)(307,360)
(308,359)(309,353)(310,354)(311,356)(312,355)(313,373)(314,374)(315,376)
(316,375)(317,381)(318,382)(319,384)(320,383)(321,377)(322,378)(323,380)
(324,379)(325,361)(326,362)(327,364)(328,363)(329,369)(330,370)(331,372)
(332,371)(333,365)(334,366)(335,368)(336,367);
s2 := Sym(384)!(  1,153)(  2,155)(  3,154)(  4,156)(  5,149)(  6,151)(  7,150)
(  8,152)(  9,145)( 10,147)( 11,146)( 12,148)( 13,165)( 14,167)( 15,166)
( 16,168)( 17,161)( 18,163)( 19,162)( 20,164)( 21,157)( 22,159)( 23,158)
( 24,160)( 25,189)( 26,191)( 27,190)( 28,192)( 29,185)( 30,187)( 31,186)
( 32,188)( 33,181)( 34,183)( 35,182)( 36,184)( 37,177)( 38,179)( 39,178)
( 40,180)( 41,173)( 42,175)( 43,174)( 44,176)( 45,169)( 46,171)( 47,170)
( 48,172)( 49,105)( 50,107)( 51,106)( 52,108)( 53,101)( 54,103)( 55,102)
( 56,104)( 57, 97)( 58, 99)( 59, 98)( 60,100)( 61,117)( 62,119)( 63,118)
( 64,120)( 65,113)( 66,115)( 67,114)( 68,116)( 69,109)( 70,111)( 71,110)
( 72,112)( 73,141)( 74,143)( 75,142)( 76,144)( 77,137)( 78,139)( 79,138)
( 80,140)( 81,133)( 82,135)( 83,134)( 84,136)( 85,129)( 86,131)( 87,130)
( 88,132)( 89,125)( 90,127)( 91,126)( 92,128)( 93,121)( 94,123)( 95,122)
( 96,124)(193,345)(194,347)(195,346)(196,348)(197,341)(198,343)(199,342)
(200,344)(201,337)(202,339)(203,338)(204,340)(205,357)(206,359)(207,358)
(208,360)(209,353)(210,355)(211,354)(212,356)(213,349)(214,351)(215,350)
(216,352)(217,381)(218,383)(219,382)(220,384)(221,377)(222,379)(223,378)
(224,380)(225,373)(226,375)(227,374)(228,376)(229,369)(230,371)(231,370)
(232,372)(233,365)(234,367)(235,366)(236,368)(237,361)(238,363)(239,362)
(240,364)(241,297)(242,299)(243,298)(244,300)(245,293)(246,295)(247,294)
(248,296)(249,289)(250,291)(251,290)(252,292)(253,309)(254,311)(255,310)
(256,312)(257,305)(258,307)(259,306)(260,308)(261,301)(262,303)(263,302)
(264,304)(265,333)(266,335)(267,334)(268,336)(269,329)(270,331)(271,330)
(272,332)(273,325)(274,327)(275,326)(276,328)(277,321)(278,323)(279,322)
(280,324)(281,317)(282,319)(283,318)(284,320)(285,313)(286,315)(287,314)
(288,316);
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*s2*s1*s0*s1*s2*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 >;

```
References : None.
to this polytope