Polytope of Type {48,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,4}*768b
if this polytope has a name.
Group : SmallGroup(768,81735)
Rank : 3
Schlafli Type : {48,4}
Number of vertices, edges, etc : 96, 192, 8
Order of s0s1s2 : 48
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {24,4}*384a
3-fold quotients : {16,4}*256b
4-fold quotients : {24,4}*192a, {12,4}*192a, {24,4}*192b
6-fold quotients : {8,4}*128a
8-fold quotients : {12,4}*96a, {24,2}*96
12-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
16-fold quotients : {12,2}*48, {6,4}*48a
24-fold quotients : {4,4}*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 := ( 1,193)( 2,195)( 3,194)( 4,196)( 5,198)( 6,197)( 7,199)( 8,201)
( 9,200)( 10,202)( 11,204)( 12,203)( 13,208)( 14,210)( 15,209)( 16,205)
( 17,207)( 18,206)( 19,214)( 20,216)( 21,215)( 22,211)( 23,213)( 24,212)
( 25,226)( 26,228)( 27,227)( 28,223)( 29,225)( 30,224)( 31,220)( 32,222)
( 33,221)( 34,217)( 35,219)( 36,218)( 37,235)( 38,237)( 39,236)( 40,238)
( 41,240)( 42,239)( 43,229)( 44,231)( 45,230)( 46,232)( 47,234)( 48,233)
( 49,253)( 50,255)( 51,254)( 52,256)( 53,258)( 54,257)( 55,259)( 56,261)
( 57,260)( 58,262)( 59,264)( 60,263)( 61,241)( 62,243)( 63,242)( 64,244)
( 65,246)( 66,245)( 67,247)( 68,249)( 69,248)( 70,250)( 71,252)( 72,251)
( 73,286)( 74,288)( 75,287)( 76,283)( 77,285)( 78,284)( 79,280)( 80,282)
( 81,281)( 82,277)( 83,279)( 84,278)( 85,274)( 86,276)( 87,275)( 88,271)
( 89,273)( 90,272)( 91,268)( 92,270)( 93,269)( 94,265)( 95,267)( 96,266)
( 97,289)( 98,291)( 99,290)(100,292)(101,294)(102,293)(103,295)(104,297)
(105,296)(106,298)(107,300)(108,299)(109,304)(110,306)(111,305)(112,301)
(113,303)(114,302)(115,310)(116,312)(117,311)(118,307)(119,309)(120,308)
(121,322)(122,324)(123,323)(124,319)(125,321)(126,320)(127,316)(128,318)
(129,317)(130,313)(131,315)(132,314)(133,331)(134,333)(135,332)(136,334)
(137,336)(138,335)(139,325)(140,327)(141,326)(142,328)(143,330)(144,329)
(145,349)(146,351)(147,350)(148,352)(149,354)(150,353)(151,355)(152,357)
(153,356)(154,358)(155,360)(156,359)(157,337)(158,339)(159,338)(160,340)
(161,342)(162,341)(163,343)(164,345)(165,344)(166,346)(167,348)(168,347)
(169,382)(170,384)(171,383)(172,379)(173,381)(174,380)(175,376)(176,378)
(177,377)(178,373)(179,375)(180,374)(181,370)(182,372)(183,371)(184,367)
(185,369)(186,368)(187,364)(188,366)(189,365)(190,361)(191,363)(192,362);;
s1 := ( 1, 3)( 4, 6)( 7, 12)( 8, 11)( 9, 10)( 13, 18)( 14, 17)( 15, 16)
( 19, 21)( 22, 24)( 25, 27)( 28, 30)( 31, 36)( 32, 35)( 33, 34)( 37, 42)
( 38, 41)( 39, 40)( 43, 45)( 46, 48)( 49, 63)( 50, 62)( 51, 61)( 52, 66)
( 53, 65)( 54, 64)( 55, 72)( 56, 71)( 57, 70)( 58, 69)( 59, 68)( 60, 67)
( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)( 79, 96)( 80, 95)
( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 97,123)( 98,122)( 99,121)(100,126)
(101,125)(102,124)(103,132)(104,131)(105,130)(106,129)(107,128)(108,127)
(109,138)(110,137)(111,136)(112,135)(113,134)(114,133)(115,141)(116,140)
(117,139)(118,144)(119,143)(120,142)(145,186)(146,185)(147,184)(148,183)
(149,182)(150,181)(151,189)(152,188)(153,187)(154,192)(155,191)(156,190)
(157,174)(158,173)(159,172)(160,171)(161,170)(162,169)(163,177)(164,176)
(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)(195,241)(196,246)
(197,245)(198,244)(199,252)(200,251)(201,250)(202,249)(203,248)(204,247)
(205,258)(206,257)(207,256)(208,255)(209,254)(210,253)(211,261)(212,260)
(213,259)(214,264)(215,263)(216,262)(217,267)(218,266)(219,265)(220,270)
(221,269)(222,268)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)
(229,282)(230,281)(231,280)(232,279)(233,278)(234,277)(235,285)(236,284)
(237,283)(238,288)(239,287)(240,286)(289,369)(290,368)(291,367)(292,372)
(293,371)(294,370)(295,366)(296,365)(297,364)(298,363)(299,362)(300,361)
(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)(307,375)(308,374)
(309,373)(310,378)(311,377)(312,376)(313,345)(314,344)(315,343)(316,348)
(317,347)(318,346)(319,342)(320,341)(321,340)(322,339)(323,338)(324,337)
(325,360)(326,359)(327,358)(328,357)(329,356)(330,355)(331,351)(332,350)
(333,349)(334,354)(335,353)(336,352);;
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)
( 25,121)( 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)
( 49,151)( 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)
( 73,175)( 74,176)( 75,177)( 76,178)( 77,179)( 78,180)( 79,169)( 80,170)
( 81,171)( 82,172)( 83,173)( 84,174)( 85,187)( 86,188)( 87,189)( 88,190)
( 89,191)( 90,192)( 91,181)( 92,182)( 93,183)( 94,184)( 95,185)( 96,186)
(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)
(241,343)(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)
(265,367)(266,368)(267,369)(268,370)(269,371)(270,372)(271,361)(272,362)
(273,363)(274,364)(275,365)(276,366)(277,379)(278,380)(279,381)(280,382)
(281,383)(282,384)(283,373)(284,374)(285,375)(286,376)(287,377)(288,378);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1,193)( 2,195)( 3,194)( 4,196)( 5,198)( 6,197)( 7,199)
( 8,201)( 9,200)( 10,202)( 11,204)( 12,203)( 13,208)( 14,210)( 15,209)
( 16,205)( 17,207)( 18,206)( 19,214)( 20,216)( 21,215)( 22,211)( 23,213)
( 24,212)( 25,226)( 26,228)( 27,227)( 28,223)( 29,225)( 30,224)( 31,220)
( 32,222)( 33,221)( 34,217)( 35,219)( 36,218)( 37,235)( 38,237)( 39,236)
( 40,238)( 41,240)( 42,239)( 43,229)( 44,231)( 45,230)( 46,232)( 47,234)
( 48,233)( 49,253)( 50,255)( 51,254)( 52,256)( 53,258)( 54,257)( 55,259)
( 56,261)( 57,260)( 58,262)( 59,264)( 60,263)( 61,241)( 62,243)( 63,242)
( 64,244)( 65,246)( 66,245)( 67,247)( 68,249)( 69,248)( 70,250)( 71,252)
( 72,251)( 73,286)( 74,288)( 75,287)( 76,283)( 77,285)( 78,284)( 79,280)
( 80,282)( 81,281)( 82,277)( 83,279)( 84,278)( 85,274)( 86,276)( 87,275)
( 88,271)( 89,273)( 90,272)( 91,268)( 92,270)( 93,269)( 94,265)( 95,267)
( 96,266)( 97,289)( 98,291)( 99,290)(100,292)(101,294)(102,293)(103,295)
(104,297)(105,296)(106,298)(107,300)(108,299)(109,304)(110,306)(111,305)
(112,301)(113,303)(114,302)(115,310)(116,312)(117,311)(118,307)(119,309)
(120,308)(121,322)(122,324)(123,323)(124,319)(125,321)(126,320)(127,316)
(128,318)(129,317)(130,313)(131,315)(132,314)(133,331)(134,333)(135,332)
(136,334)(137,336)(138,335)(139,325)(140,327)(141,326)(142,328)(143,330)
(144,329)(145,349)(146,351)(147,350)(148,352)(149,354)(150,353)(151,355)
(152,357)(153,356)(154,358)(155,360)(156,359)(157,337)(158,339)(159,338)
(160,340)(161,342)(162,341)(163,343)(164,345)(165,344)(166,346)(167,348)
(168,347)(169,382)(170,384)(171,383)(172,379)(173,381)(174,380)(175,376)
(176,378)(177,377)(178,373)(179,375)(180,374)(181,370)(182,372)(183,371)
(184,367)(185,369)(186,368)(187,364)(188,366)(189,365)(190,361)(191,363)
(192,362);
s1 := Sym(384)!( 1, 3)( 4, 6)( 7, 12)( 8, 11)( 9, 10)( 13, 18)( 14, 17)
( 15, 16)( 19, 21)( 22, 24)( 25, 27)( 28, 30)( 31, 36)( 32, 35)( 33, 34)
( 37, 42)( 38, 41)( 39, 40)( 43, 45)( 46, 48)( 49, 63)( 50, 62)( 51, 61)
( 52, 66)( 53, 65)( 54, 64)( 55, 72)( 56, 71)( 57, 70)( 58, 69)( 59, 68)
( 60, 67)( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)( 79, 96)
( 80, 95)( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 97,123)( 98,122)( 99,121)
(100,126)(101,125)(102,124)(103,132)(104,131)(105,130)(106,129)(107,128)
(108,127)(109,138)(110,137)(111,136)(112,135)(113,134)(114,133)(115,141)
(116,140)(117,139)(118,144)(119,143)(120,142)(145,186)(146,185)(147,184)
(148,183)(149,182)(150,181)(151,189)(152,188)(153,187)(154,192)(155,191)
(156,190)(157,174)(158,173)(159,172)(160,171)(161,170)(162,169)(163,177)
(164,176)(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)(195,241)
(196,246)(197,245)(198,244)(199,252)(200,251)(201,250)(202,249)(203,248)
(204,247)(205,258)(206,257)(207,256)(208,255)(209,254)(210,253)(211,261)
(212,260)(213,259)(214,264)(215,263)(216,262)(217,267)(218,266)(219,265)
(220,270)(221,269)(222,268)(223,276)(224,275)(225,274)(226,273)(227,272)
(228,271)(229,282)(230,281)(231,280)(232,279)(233,278)(234,277)(235,285)
(236,284)(237,283)(238,288)(239,287)(240,286)(289,369)(290,368)(291,367)
(292,372)(293,371)(294,370)(295,366)(296,365)(297,364)(298,363)(299,362)
(300,361)(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)(307,375)
(308,374)(309,373)(310,378)(311,377)(312,376)(313,345)(314,344)(315,343)
(316,348)(317,347)(318,346)(319,342)(320,341)(321,340)(322,339)(323,338)
(324,337)(325,360)(326,359)(327,358)(328,357)(329,356)(330,355)(331,351)
(332,350)(333,349)(334,354)(335,353)(336,352);
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)( 25,121)( 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)( 49,151)( 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)( 73,175)( 74,176)( 75,177)( 76,178)( 77,179)( 78,180)( 79,169)
( 80,170)( 81,171)( 82,172)( 83,173)( 84,174)( 85,187)( 86,188)( 87,189)
( 88,190)( 89,191)( 90,192)( 91,181)( 92,182)( 93,183)( 94,184)( 95,185)
( 96,186)(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)(241,343)(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)(265,367)(266,368)(267,369)(268,370)(269,371)(270,372)(271,361)
(272,362)(273,363)(274,364)(275,365)(276,366)(277,379)(278,380)(279,381)
(280,382)(281,383)(282,384)(283,373)(284,374)(285,375)(286,376)(287,377)
(288,378);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0 >;
References : None.
to this polytope