Polytope of Type {48,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,8}*768f
if this polytope has a name.
Group : SmallGroup(768,83050)
Rank : 3
Schlafli Type : {48,8}
Number of vertices, edges, etc : 48, 192, 8
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 4
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}*384b
   3-fold quotients : {16,8}*256f
   4-fold quotients : {24,4}*192a, {12,8}*192a
   6-fold quotients : {8,8}*128b, {16,4}*128b
   8-fold quotients : {12,4}*96a, {24,2}*96, {6,8}*96
   12-fold quotients : {4,8}*64a, {8,4}*64a
   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)
( 25,316)( 26,318)( 27,317)( 28,313)( 29,315)( 30,314)( 31,322)( 32,324)
( 33,323)( 34,319)( 35,321)( 36,320)( 37,325)( 38,327)( 39,326)( 40,328)
( 41,330)( 42,329)( 43,331)( 44,333)( 45,332)( 46,334)( 47,336)( 48,335)
( 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)
( 73,382)( 74,384)( 75,383)( 76,379)( 77,381)( 78,380)( 79,376)( 80,378)
( 81,377)( 82,373)( 83,375)( 84,374)( 85,370)( 86,372)( 87,371)( 88,367)
( 89,369)( 90,368)( 91,364)( 92,366)( 93,365)( 94,361)( 95,363)( 96,362)
( 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)
(121,220)(122,222)(123,221)(124,217)(125,219)(126,218)(127,226)(128,228)
(129,227)(130,223)(131,225)(132,224)(133,229)(134,231)(135,230)(136,232)
(137,234)(138,233)(139,235)(140,237)(141,236)(142,238)(143,240)(144,239)
(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)
(169,286)(170,288)(171,287)(172,283)(173,285)(174,284)(175,280)(176,282)
(177,281)(178,277)(179,279)(180,278)(181,274)(182,276)(183,275)(184,271)
(185,273)(186,272)(187,268)(188,270)(189,269)(190,265)(191,267)(192,266);;
s1 := (  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)( 19, 24)
( 20, 23)( 21, 22)( 25, 36)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)
( 37, 45)( 38, 44)( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 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, 96)( 74, 95)( 75, 94)( 76, 93)( 77, 92)( 78, 91)
( 79, 90)( 80, 89)( 81, 88)( 82, 87)( 83, 86)( 84, 85)( 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)(217,276)(218,275)
(219,274)(220,273)(221,272)(222,271)(223,270)(224,269)(225,268)(226,267)
(227,266)(228,265)(229,285)(230,284)(231,283)(232,288)(233,287)(234,286)
(235,279)(236,278)(237,277)(238,282)(239,281)(240,280)(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)
( 25,130)( 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);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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*s2*s1*s0*s1*s0*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 ];;
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)( 25,316)( 26,318)( 27,317)( 28,313)( 29,315)( 30,314)( 31,322)
( 32,324)( 33,323)( 34,319)( 35,321)( 36,320)( 37,325)( 38,327)( 39,326)
( 40,328)( 41,330)( 42,329)( 43,331)( 44,333)( 45,332)( 46,334)( 47,336)
( 48,335)( 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)( 73,382)( 74,384)( 75,383)( 76,379)( 77,381)( 78,380)( 79,376)
( 80,378)( 81,377)( 82,373)( 83,375)( 84,374)( 85,370)( 86,372)( 87,371)
( 88,367)( 89,369)( 90,368)( 91,364)( 92,366)( 93,365)( 94,361)( 95,363)
( 96,362)( 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)(121,220)(122,222)(123,221)(124,217)(125,219)(126,218)(127,226)
(128,228)(129,227)(130,223)(131,225)(132,224)(133,229)(134,231)(135,230)
(136,232)(137,234)(138,233)(139,235)(140,237)(141,236)(142,238)(143,240)
(144,239)(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)(169,286)(170,288)(171,287)(172,283)(173,285)(174,284)(175,280)
(176,282)(177,281)(178,277)(179,279)(180,278)(181,274)(182,276)(183,275)
(184,271)(185,273)(186,272)(187,268)(188,270)(189,269)(190,265)(191,267)
(192,266);
s1 := Sym(384)!(  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)
( 19, 24)( 20, 23)( 21, 22)( 25, 36)( 26, 35)( 27, 34)( 28, 33)( 29, 32)
( 30, 31)( 37, 45)( 38, 44)( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 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, 96)( 74, 95)( 75, 94)( 76, 93)( 77, 92)
( 78, 91)( 79, 90)( 80, 89)( 81, 88)( 82, 87)( 83, 86)( 84, 85)( 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)(217,276)
(218,275)(219,274)(220,273)(221,272)(222,271)(223,270)(224,269)(225,268)
(226,267)(227,266)(228,265)(229,285)(230,284)(231,283)(232,288)(233,287)
(234,286)(235,279)(236,278)(237,277)(238,282)(239,281)(240,280)(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)( 25,130)( 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);
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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*s2*s1*s0*s1*s0*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 >;

References : None.
to this polytope