Polytope of Type {4,48}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,48}*768a
if this polytope has a name.
Group : SmallGroup(768,81667)
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 : {4,24}*384a, {4,48}*384a, {4,48}*384b
3-fold quotients : {4,16}*256a
4-fold quotients : {4,24}*192a, {4,12}*192a, {4,24}*192b, {2,48}*192
6-fold quotients : {4,8}*128a, {4,16}*128a, {4,16}*128b
8-fold quotients : {4,12}*96a, {2,24}*96
12-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64, {2,16}*64
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)
( 25,121)( 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);;
s1 := ( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 19, 22)
( 20, 24)( 21, 23)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 37, 40)( 38, 42)
( 39, 41)( 43, 46)( 44, 48)( 45, 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, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)( 78, 89)( 79, 91)( 80, 93)
( 81, 92)( 82, 94)( 83, 96)( 84, 95)( 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)(217,265)(218,267)(219,266)(220,268)
(221,270)(222,269)(223,271)(224,273)(225,272)(226,274)(227,276)(228,275)
(229,280)(230,282)(231,281)(232,277)(233,279)(234,278)(235,286)(236,288)
(237,287)(238,283)(239,285)(240,284)(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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*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, 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);
s1 := Sym(384)!( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 37, 40)
( 38, 42)( 39, 41)( 43, 46)( 44, 48)( 45, 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, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)( 78, 89)( 79, 91)
( 80, 93)( 81, 92)( 82, 94)( 83, 96)( 84, 95)( 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)(217,265)(218,267)(219,266)
(220,268)(221,270)(222,269)(223,271)(224,273)(225,272)(226,274)(227,276)
(228,275)(229,280)(230,282)(231,281)(232,277)(233,279)(234,278)(235,286)
(236,288)(237,287)(238,283)(239,285)(240,284)(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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*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