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# Polytope of Type {48,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,8}*768d
Also Known As : {48,8|2}. if this polytope has another name.
Group : SmallGroup(768,82994)
Rank : 3
Schlafli Type : {48,8}
Number of vertices, edges, etc : 48, 192, 8
Order of s0s1s2 : 48
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {24,8}*384b, {48,4}*384a
3-fold quotients : {16,8}*256d
4-fold quotients : {24,4}*192a, {12,8}*192a, {48,2}*192
6-fold quotients : {8,8}*128b, {16,4}*128a
8-fold quotients : {12,4}*96a, {24,2}*96, {6,8}*96
12-fold quotients : {4,8}*64a, {8,4}*64a, {16,2}*64
16-fold quotients : {12,2}*48, {6,4}*48a
24-fold quotients : {4,4}*32, {2,8}*32, {8,2}*32
32-fold quotients : {6,2}*24
48-fold quotients : {2,4}*16, {4,2}*16
64-fold quotients : {3,2}*12
96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  1,289)(  2,291)(  3,290)(  4,292)(  5,294)(  6,293)(  7,295)(  8,297)
(  9,296)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)( 16,301)
( 17,303)( 18,302)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)( 24,308)
( 25,313)( 26,315)( 27,314)( 28,316)( 29,318)( 30,317)( 31,319)( 32,321)
( 33,320)( 34,322)( 35,324)( 36,323)( 37,328)( 38,330)( 39,329)( 40,325)
( 41,327)( 42,326)( 43,334)( 44,336)( 45,335)( 46,331)( 47,333)( 48,332)
( 49,355)( 50,357)( 51,356)( 52,358)( 53,360)( 54,359)( 55,349)( 56,351)
( 57,350)( 58,352)( 59,354)( 60,353)( 61,343)( 62,345)( 63,344)( 64,346)
( 65,348)( 66,347)( 67,337)( 68,339)( 69,338)( 70,340)( 71,342)( 72,341)
( 73,379)( 74,381)( 75,380)( 76,382)( 77,384)( 78,383)( 79,373)( 80,375)
( 81,374)( 82,376)( 83,378)( 84,377)( 85,367)( 86,369)( 87,368)( 88,370)
( 89,372)( 90,371)( 91,361)( 92,363)( 93,362)( 94,364)( 95,366)( 96,365)
( 97,193)( 98,195)( 99,194)(100,196)(101,198)(102,197)(103,199)(104,201)
(105,200)(106,202)(107,204)(108,203)(109,208)(110,210)(111,209)(112,205)
(113,207)(114,206)(115,214)(116,216)(117,215)(118,211)(119,213)(120,212)
(121,217)(122,219)(123,218)(124,220)(125,222)(126,221)(127,223)(128,225)
(129,224)(130,226)(131,228)(132,227)(133,232)(134,234)(135,233)(136,229)
(137,231)(138,230)(139,238)(140,240)(141,239)(142,235)(143,237)(144,236)
(145,259)(146,261)(147,260)(148,262)(149,264)(150,263)(151,253)(152,255)
(153,254)(154,256)(155,258)(156,257)(157,247)(158,249)(159,248)(160,250)
(161,252)(162,251)(163,241)(164,243)(165,242)(166,244)(167,246)(168,245)
(169,283)(170,285)(171,284)(172,286)(173,288)(174,287)(175,277)(176,279)
(177,278)(178,280)(179,282)(180,281)(181,271)(182,273)(183,272)(184,274)
(185,276)(186,275)(187,265)(188,267)(189,266)(190,268)(191,270)(192,269);;
s1 := (  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)( 19, 24)
( 20, 23)( 21, 22)( 25, 33)( 26, 32)( 27, 31)( 28, 36)( 29, 35)( 30, 34)
( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 49, 63)( 50, 62)
( 51, 61)( 52, 66)( 53, 65)( 54, 64)( 55, 69)( 56, 68)( 57, 67)( 58, 72)
( 59, 71)( 60, 70)( 73, 93)( 74, 92)( 75, 91)( 76, 96)( 77, 95)( 78, 94)
( 79, 87)( 80, 86)( 81, 85)( 82, 90)( 83, 89)( 84, 88)( 97,123)( 98,122)
( 99,121)(100,126)(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)
(107,131)(108,130)(109,138)(110,137)(111,136)(112,135)(113,134)(114,133)
(115,144)(116,143)(117,142)(118,141)(119,140)(120,139)(145,183)(146,182)
(147,181)(148,186)(149,185)(150,184)(151,189)(152,188)(153,187)(154,192)
(155,191)(156,190)(157,171)(158,170)(159,169)(160,174)(161,173)(162,172)
(163,177)(164,176)(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)
(195,241)(196,246)(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)
(203,251)(204,250)(205,258)(206,257)(207,256)(208,255)(209,254)(210,253)
(211,264)(212,263)(213,262)(214,261)(215,260)(216,259)(217,273)(218,272)
(219,271)(220,276)(221,275)(222,274)(223,267)(224,266)(225,265)(226,270)
(227,269)(228,268)(229,288)(230,287)(231,286)(232,285)(233,284)(234,283)
(235,282)(236,281)(237,280)(238,279)(239,278)(240,277)(289,369)(290,368)
(291,367)(292,372)(293,371)(294,370)(295,363)(296,362)(297,361)(298,366)
(299,365)(300,364)(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)
(307,378)(308,377)(309,376)(310,375)(311,374)(312,373)(313,345)(314,344)
(315,343)(316,348)(317,347)(318,346)(319,339)(320,338)(321,337)(322,342)
(323,341)(324,340)(325,360)(326,359)(327,358)(328,357)(329,356)(330,355)
(331,354)(332,353)(333,352)(334,351)(335,350)(336,349);;
s2 := (  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)
( 25,127)( 26,128)( 27,129)( 28,130)( 29,131)( 30,132)( 31,121)( 32,122)
( 33,123)( 34,124)( 35,125)( 36,126)( 37,139)( 38,140)( 39,141)( 40,142)
( 41,143)( 42,144)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)
( 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)
( 73,169)( 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)
(217,319)(218,320)(219,321)(220,322)(221,323)(222,324)(223,313)(224,314)
(225,315)(226,316)(227,317)(228,318)(229,331)(230,332)(231,333)(232,334)
(233,335)(234,336)(235,325)(236,326)(237,327)(238,328)(239,329)(240,330)
(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)
(265,361)(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);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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)!(  1,289)(  2,291)(  3,290)(  4,292)(  5,294)(  6,293)(  7,295)
(  8,297)(  9,296)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)
( 16,301)( 17,303)( 18,302)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)
( 24,308)( 25,313)( 26,315)( 27,314)( 28,316)( 29,318)( 30,317)( 31,319)
( 32,321)( 33,320)( 34,322)( 35,324)( 36,323)( 37,328)( 38,330)( 39,329)
( 40,325)( 41,327)( 42,326)( 43,334)( 44,336)( 45,335)( 46,331)( 47,333)
( 48,332)( 49,355)( 50,357)( 51,356)( 52,358)( 53,360)( 54,359)( 55,349)
( 56,351)( 57,350)( 58,352)( 59,354)( 60,353)( 61,343)( 62,345)( 63,344)
( 64,346)( 65,348)( 66,347)( 67,337)( 68,339)( 69,338)( 70,340)( 71,342)
( 72,341)( 73,379)( 74,381)( 75,380)( 76,382)( 77,384)( 78,383)( 79,373)
( 80,375)( 81,374)( 82,376)( 83,378)( 84,377)( 85,367)( 86,369)( 87,368)
( 88,370)( 89,372)( 90,371)( 91,361)( 92,363)( 93,362)( 94,364)( 95,366)
( 96,365)( 97,193)( 98,195)( 99,194)(100,196)(101,198)(102,197)(103,199)
(104,201)(105,200)(106,202)(107,204)(108,203)(109,208)(110,210)(111,209)
(112,205)(113,207)(114,206)(115,214)(116,216)(117,215)(118,211)(119,213)
(120,212)(121,217)(122,219)(123,218)(124,220)(125,222)(126,221)(127,223)
(128,225)(129,224)(130,226)(131,228)(132,227)(133,232)(134,234)(135,233)
(136,229)(137,231)(138,230)(139,238)(140,240)(141,239)(142,235)(143,237)
(144,236)(145,259)(146,261)(147,260)(148,262)(149,264)(150,263)(151,253)
(152,255)(153,254)(154,256)(155,258)(156,257)(157,247)(158,249)(159,248)
(160,250)(161,252)(162,251)(163,241)(164,243)(165,242)(166,244)(167,246)
(168,245)(169,283)(170,285)(171,284)(172,286)(173,288)(174,287)(175,277)
(176,279)(177,278)(178,280)(179,282)(180,281)(181,271)(182,273)(183,272)
(184,274)(185,276)(186,275)(187,265)(188,267)(189,266)(190,268)(191,270)
(192,269);
s1 := Sym(384)!(  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)
( 19, 24)( 20, 23)( 21, 22)( 25, 33)( 26, 32)( 27, 31)( 28, 36)( 29, 35)
( 30, 34)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 49, 63)
( 50, 62)( 51, 61)( 52, 66)( 53, 65)( 54, 64)( 55, 69)( 56, 68)( 57, 67)
( 58, 72)( 59, 71)( 60, 70)( 73, 93)( 74, 92)( 75, 91)( 76, 96)( 77, 95)
( 78, 94)( 79, 87)( 80, 86)( 81, 85)( 82, 90)( 83, 89)( 84, 88)( 97,123)
( 98,122)( 99,121)(100,126)(101,125)(102,124)(103,129)(104,128)(105,127)
(106,132)(107,131)(108,130)(109,138)(110,137)(111,136)(112,135)(113,134)
(114,133)(115,144)(116,143)(117,142)(118,141)(119,140)(120,139)(145,183)
(146,182)(147,181)(148,186)(149,185)(150,184)(151,189)(152,188)(153,187)
(154,192)(155,191)(156,190)(157,171)(158,170)(159,169)(160,174)(161,173)
(162,172)(163,177)(164,176)(165,175)(166,180)(167,179)(168,178)(193,243)
(194,242)(195,241)(196,246)(197,245)(198,244)(199,249)(200,248)(201,247)
(202,252)(203,251)(204,250)(205,258)(206,257)(207,256)(208,255)(209,254)
(210,253)(211,264)(212,263)(213,262)(214,261)(215,260)(216,259)(217,273)
(218,272)(219,271)(220,276)(221,275)(222,274)(223,267)(224,266)(225,265)
(226,270)(227,269)(228,268)(229,288)(230,287)(231,286)(232,285)(233,284)
(234,283)(235,282)(236,281)(237,280)(238,279)(239,278)(240,277)(289,369)
(290,368)(291,367)(292,372)(293,371)(294,370)(295,363)(296,362)(297,361)
(298,366)(299,365)(300,364)(301,384)(302,383)(303,382)(304,381)(305,380)
(306,379)(307,378)(308,377)(309,376)(310,375)(311,374)(312,373)(313,345)
(314,344)(315,343)(316,348)(317,347)(318,346)(319,339)(320,338)(321,337)
(322,342)(323,341)(324,340)(325,360)(326,359)(327,358)(328,357)(329,356)
(330,355)(331,354)(332,353)(333,352)(334,351)(335,350)(336,349);
s2 := 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)( 25,127)( 26,128)( 27,129)( 28,130)( 29,131)( 30,132)( 31,121)
( 32,122)( 33,123)( 34,124)( 35,125)( 36,126)( 37,139)( 38,140)( 39,141)
( 40,142)( 41,143)( 42,144)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)
( 48,138)( 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)( 73,169)( 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)(217,319)(218,320)(219,321)(220,322)(221,323)(222,324)(223,313)
(224,314)(225,315)(226,316)(227,317)(228,318)(229,331)(230,332)(231,333)
(232,334)(233,335)(234,336)(235,325)(236,326)(237,327)(238,328)(239,329)
(240,330)(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)(265,361)(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);
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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