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# Polytope of Type {8,48}

Atlas Canonical Name : {8,48}*768e
if this polytope has a name.
Group : SmallGroup(768,83050)
Rank : 3
Schlafli Type : {8,48}
Number of vertices, edges, etc : 8, 192, 48
Order of s0s1s2 : 48
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 : {8,24}*384a, {4,48}*384b
3-fold quotients : {8,16}*256e
4-fold quotients : {4,24}*192a, {8,12}*192b
6-fold quotients : {8,8}*128a, {4,16}*128b
8-fold quotients : {4,12}*96a, {2,24}*96
12-fold quotients : {4,8}*64a, {8,4}*64b
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)
( 25,130)( 26,131)( 27,132)( 28,127)( 29,128)( 30,129)( 31,124)( 32,125)
( 33,126)( 34,121)( 35,122)( 36,123)( 37,142)( 38,143)( 39,144)( 40,139)
( 41,140)( 42,141)( 43,136)( 44,137)( 45,138)( 46,133)( 47,134)( 48,135)
( 49,151)( 50,152)( 51,153)( 52,154)( 53,155)( 54,156)( 55,145)( 56,146)
( 57,147)( 58,148)( 59,149)( 60,150)( 61,163)( 62,164)( 63,165)( 64,166)
( 65,167)( 66,168)( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)( 72,162)
( 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)
(217,322)(218,323)(219,324)(220,319)(221,320)(222,321)(223,316)(224,317)
(225,318)(226,313)(227,314)(228,315)(229,334)(230,335)(231,336)(232,331)
(233,332)(234,333)(235,328)(236,329)(237,330)(238,325)(239,326)(240,327)
(241,343)(242,344)(243,345)(244,346)(245,347)(246,348)(247,337)(248,338)
(249,339)(250,340)(251,341)(252,342)(253,355)(254,356)(255,357)(256,358)
(257,359)(258,360)(259,349)(260,350)(261,351)(262,352)(263,353)(264,354)
(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)(  8,  9)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 19, 22)
( 20, 24)( 21, 23)( 25, 34)( 26, 36)( 27, 35)( 28, 31)( 29, 33)( 30, 32)
( 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, 67)( 56, 69)( 57, 68)( 58, 70)
( 59, 72)( 60, 71)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)
( 79, 88)( 80, 90)( 81, 89)( 82, 85)( 83, 87)( 84, 86)( 97,121)( 98,123)
( 99,122)(100,124)(101,126)(102,125)(103,127)(104,129)(105,128)(106,130)
(107,132)(108,131)(109,136)(110,138)(111,137)(112,133)(113,135)(114,134)
(115,142)(116,144)(117,143)(118,139)(119,141)(120,140)(145,181)(146,183)
(147,182)(148,184)(149,186)(150,185)(151,187)(152,189)(153,188)(154,190)
(155,192)(156,191)(157,169)(158,171)(159,170)(160,172)(161,174)(162,173)
(163,175)(164,177)(165,176)(166,178)(167,180)(168,179)(193,241)(194,243)
(195,242)(196,244)(197,246)(198,245)(199,247)(200,249)(201,248)(202,250)
(203,252)(204,251)(205,256)(206,258)(207,257)(208,253)(209,255)(210,254)
(211,262)(212,264)(213,263)(214,259)(215,261)(216,260)(217,274)(218,276)
(219,275)(220,271)(221,273)(222,272)(223,268)(224,270)(225,269)(226,265)
(227,267)(228,266)(229,283)(230,285)(231,284)(232,286)(233,288)(234,287)
(235,277)(236,279)(237,278)(238,280)(239,282)(240,281)(289,367)(290,369)
(291,368)(292,370)(293,372)(294,371)(295,361)(296,363)(297,362)(298,364)
(299,366)(300,365)(301,382)(302,384)(303,383)(304,379)(305,381)(306,380)
(307,376)(308,378)(309,377)(310,373)(311,375)(312,374)(313,343)(314,345)
(315,344)(316,346)(317,348)(318,347)(319,337)(320,339)(321,338)(322,340)
(323,342)(324,341)(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)(  7,201)(  8,200)
(  9,199)( 10,204)( 11,203)( 12,202)( 13,210)( 14,209)( 15,208)( 16,207)
( 17,206)( 18,205)( 19,216)( 20,215)( 21,214)( 22,213)( 23,212)( 24,211)
( 25,225)( 26,224)( 27,223)( 28,228)( 29,227)( 30,226)( 31,219)( 32,218)
( 33,217)( 34,222)( 35,221)( 36,220)( 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)( 55,261)( 56,260)
( 57,259)( 58,264)( 59,263)( 60,262)( 61,243)( 62,242)( 63,241)( 64,246)
( 65,245)( 66,244)( 67,249)( 68,248)( 69,247)( 70,252)( 71,251)( 72,250)
( 73,285)( 74,284)( 75,283)( 76,288)( 77,287)( 78,286)( 79,279)( 80,278)
( 81,277)( 82,282)( 83,281)( 84,280)( 85,273)( 86,272)( 87,271)( 88,276)
( 89,275)( 90,274)( 91,267)( 92,266)( 93,265)( 94,270)( 95,269)( 96,268)
( 97,291)( 98,290)( 99,289)(100,294)(101,293)(102,292)(103,297)(104,296)
(105,295)(106,300)(107,299)(108,298)(109,306)(110,305)(111,304)(112,303)
(113,302)(114,301)(115,312)(116,311)(117,310)(118,309)(119,308)(120,307)
(121,321)(122,320)(123,319)(124,324)(125,323)(126,322)(127,315)(128,314)
(129,313)(130,318)(131,317)(132,316)(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)(151,357)(152,356)
(153,355)(154,360)(155,359)(156,358)(157,339)(158,338)(159,337)(160,342)
(161,341)(162,340)(163,345)(164,344)(165,343)(166,348)(167,347)(168,346)
(169,381)(170,380)(171,379)(172,384)(173,383)(174,382)(175,375)(176,374)
(177,373)(178,378)(179,377)(180,376)(181,369)(182,368)(183,367)(184,372)
(185,371)(186,370)(187,363)(188,362)(189,361)(190,366)(191,365)(192,364);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*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*s0*s1*s2*s1*s2*s1*s2*s0*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)( 25,130)( 26,131)( 27,132)( 28,127)( 29,128)( 30,129)( 31,124)
( 32,125)( 33,126)( 34,121)( 35,122)( 36,123)( 37,142)( 38,143)( 39,144)
( 40,139)( 41,140)( 42,141)( 43,136)( 44,137)( 45,138)( 46,133)( 47,134)
( 48,135)( 49,151)( 50,152)( 51,153)( 52,154)( 53,155)( 54,156)( 55,145)
( 56,146)( 57,147)( 58,148)( 59,149)( 60,150)( 61,163)( 62,164)( 63,165)
( 64,166)( 65,167)( 66,168)( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)
( 72,162)( 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)(217,322)(218,323)(219,324)(220,319)(221,320)(222,321)(223,316)
(224,317)(225,318)(226,313)(227,314)(228,315)(229,334)(230,335)(231,336)
(232,331)(233,332)(234,333)(235,328)(236,329)(237,330)(238,325)(239,326)
(240,327)(241,343)(242,344)(243,345)(244,346)(245,347)(246,348)(247,337)
(248,338)(249,339)(250,340)(251,341)(252,342)(253,355)(254,356)(255,357)
(256,358)(257,359)(258,360)(259,349)(260,350)(261,351)(262,352)(263,353)
(264,354)(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)(  8,  9)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 19, 22)( 20, 24)( 21, 23)( 25, 34)( 26, 36)( 27, 35)( 28, 31)( 29, 33)
( 30, 32)( 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, 67)( 56, 69)( 57, 68)
( 58, 70)( 59, 72)( 60, 71)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)
( 78, 92)( 79, 88)( 80, 90)( 81, 89)( 82, 85)( 83, 87)( 84, 86)( 97,121)
( 98,123)( 99,122)(100,124)(101,126)(102,125)(103,127)(104,129)(105,128)
(106,130)(107,132)(108,131)(109,136)(110,138)(111,137)(112,133)(113,135)
(114,134)(115,142)(116,144)(117,143)(118,139)(119,141)(120,140)(145,181)
(146,183)(147,182)(148,184)(149,186)(150,185)(151,187)(152,189)(153,188)
(154,190)(155,192)(156,191)(157,169)(158,171)(159,170)(160,172)(161,174)
(162,173)(163,175)(164,177)(165,176)(166,178)(167,180)(168,179)(193,241)
(194,243)(195,242)(196,244)(197,246)(198,245)(199,247)(200,249)(201,248)
(202,250)(203,252)(204,251)(205,256)(206,258)(207,257)(208,253)(209,255)
(210,254)(211,262)(212,264)(213,263)(214,259)(215,261)(216,260)(217,274)
(218,276)(219,275)(220,271)(221,273)(222,272)(223,268)(224,270)(225,269)
(226,265)(227,267)(228,266)(229,283)(230,285)(231,284)(232,286)(233,288)
(234,287)(235,277)(236,279)(237,278)(238,280)(239,282)(240,281)(289,367)
(290,369)(291,368)(292,370)(293,372)(294,371)(295,361)(296,363)(297,362)
(298,364)(299,366)(300,365)(301,382)(302,384)(303,383)(304,379)(305,381)
(306,380)(307,376)(308,378)(309,377)(310,373)(311,375)(312,374)(313,343)
(314,345)(315,344)(316,346)(317,348)(318,347)(319,337)(320,339)(321,338)
(322,340)(323,342)(324,341)(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)(  7,201)
(  8,200)(  9,199)( 10,204)( 11,203)( 12,202)( 13,210)( 14,209)( 15,208)
( 16,207)( 17,206)( 18,205)( 19,216)( 20,215)( 21,214)( 22,213)( 23,212)
( 24,211)( 25,225)( 26,224)( 27,223)( 28,228)( 29,227)( 30,226)( 31,219)
( 32,218)( 33,217)( 34,222)( 35,221)( 36,220)( 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)( 55,261)
( 56,260)( 57,259)( 58,264)( 59,263)( 60,262)( 61,243)( 62,242)( 63,241)
( 64,246)( 65,245)( 66,244)( 67,249)( 68,248)( 69,247)( 70,252)( 71,251)
( 72,250)( 73,285)( 74,284)( 75,283)( 76,288)( 77,287)( 78,286)( 79,279)
( 80,278)( 81,277)( 82,282)( 83,281)( 84,280)( 85,273)( 86,272)( 87,271)
( 88,276)( 89,275)( 90,274)( 91,267)( 92,266)( 93,265)( 94,270)( 95,269)
( 96,268)( 97,291)( 98,290)( 99,289)(100,294)(101,293)(102,292)(103,297)
(104,296)(105,295)(106,300)(107,299)(108,298)(109,306)(110,305)(111,304)
(112,303)(113,302)(114,301)(115,312)(116,311)(117,310)(118,309)(119,308)
(120,307)(121,321)(122,320)(123,319)(124,324)(125,323)(126,322)(127,315)
(128,314)(129,313)(130,318)(131,317)(132,316)(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)(151,357)
(152,356)(153,355)(154,360)(155,359)(156,358)(157,339)(158,338)(159,337)
(160,342)(161,341)(162,340)(163,345)(164,344)(165,343)(166,348)(167,347)
(168,346)(169,381)(170,380)(171,379)(172,384)(173,383)(174,382)(175,375)
(176,374)(177,373)(178,378)(179,377)(180,376)(181,369)(182,368)(183,367)
(184,372)(185,371)(186,370)(187,363)(188,362)(189,361)(190,366)(191,365)
(192,364);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*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*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2 >;

```
References : None.
to this polytope