Polytope of Type {24,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*768a
if this polytope has a name.
Group : SmallGroup(768,81599)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 96, 192, 16
Order of s0s1s2 : 24
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, {12,4}*384a, {24,4}*384b
3-fold quotients : {8,4}*256a
4-fold quotients : {24,4}*192a, {12,4}*192a, {24,4}*192b
6-fold quotients : {8,4}*128a, {4,4}*128, {8,4}*128b
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)( 13,205)( 14,207)( 15,206)( 16,208)
( 17,210)( 18,209)( 19,211)( 20,213)( 21,212)( 22,214)( 23,216)( 24,215)
( 25,226)( 26,228)( 27,227)( 28,223)( 29,225)( 30,224)( 31,220)( 32,222)
( 33,221)( 34,217)( 35,219)( 36,218)( 37,238)( 38,240)( 39,239)( 40,235)
( 41,237)( 42,236)( 43,232)( 44,234)( 45,233)( 46,229)( 47,231)( 48,230)
( 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)(109,301)(110,303)(111,302)(112,304)
(113,306)(114,305)(115,307)(116,309)(117,308)(118,310)(119,312)(120,311)
(121,322)(122,324)(123,323)(124,319)(125,321)(126,320)(127,316)(128,318)
(129,317)(130,313)(131,315)(132,314)(133,334)(134,336)(135,335)(136,331)
(137,333)(138,332)(139,328)(140,330)(141,329)(142,325)(143,327)(144,326)
(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, 15)( 16, 18)( 19, 24)
( 20, 23)( 21, 22)( 25, 27)( 28, 30)( 31, 36)( 32, 35)( 33, 34)( 37, 39)
( 40, 42)( 43, 48)( 44, 47)( 45, 46)( 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)
(109,135)(110,134)(111,133)(112,138)(113,137)(114,136)(115,144)(116,143)
(117,142)(118,141)(119,140)(120,139)(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)
(205,255)(206,254)(207,253)(208,258)(209,257)(210,256)(211,264)(212,263)
(213,262)(214,261)(215,260)(216,259)(217,267)(218,266)(219,265)(220,270)
(221,269)(222,268)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)
(229,279)(230,278)(231,277)(232,282)(233,281)(234,280)(235,288)(236,287)
(237,286)(238,285)(239,284)(240,283)(289,369)(290,368)(291,367)(292,372)
(293,371)(294,370)(295,366)(296,365)(297,364)(298,363)(299,362)(300,361)
(301,381)(302,380)(303,379)(304,384)(305,383)(306,382)(307,378)(308,377)
(309,376)(310,375)(311,374)(312,373)(313,345)(314,344)(315,343)(316,348)
(317,347)(318,346)(319,342)(320,341)(321,340)(322,339)(323,338)(324,337)
(325,357)(326,356)(327,355)(328,360)(329,359)(330,358)(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)
( 25,121)( 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,
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)!( 1,193)( 2,195)( 3,194)( 4,196)( 5,198)( 6,197)( 7,199)
( 8,201)( 9,200)( 10,202)( 11,204)( 12,203)( 13,205)( 14,207)( 15,206)
( 16,208)( 17,210)( 18,209)( 19,211)( 20,213)( 21,212)( 22,214)( 23,216)
( 24,215)( 25,226)( 26,228)( 27,227)( 28,223)( 29,225)( 30,224)( 31,220)
( 32,222)( 33,221)( 34,217)( 35,219)( 36,218)( 37,238)( 38,240)( 39,239)
( 40,235)( 41,237)( 42,236)( 43,232)( 44,234)( 45,233)( 46,229)( 47,231)
( 48,230)( 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)(109,301)(110,303)(111,302)
(112,304)(113,306)(114,305)(115,307)(116,309)(117,308)(118,310)(119,312)
(120,311)(121,322)(122,324)(123,323)(124,319)(125,321)(126,320)(127,316)
(128,318)(129,317)(130,313)(131,315)(132,314)(133,334)(134,336)(135,335)
(136,331)(137,333)(138,332)(139,328)(140,330)(141,329)(142,325)(143,327)
(144,326)(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, 15)( 16, 18)
( 19, 24)( 20, 23)( 21, 22)( 25, 27)( 28, 30)( 31, 36)( 32, 35)( 33, 34)
( 37, 39)( 40, 42)( 43, 48)( 44, 47)( 45, 46)( 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)(109,135)(110,134)(111,133)(112,138)(113,137)(114,136)(115,144)
(116,143)(117,142)(118,141)(119,140)(120,139)(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)(205,255)(206,254)(207,253)(208,258)(209,257)(210,256)(211,264)
(212,263)(213,262)(214,261)(215,260)(216,259)(217,267)(218,266)(219,265)
(220,270)(221,269)(222,268)(223,276)(224,275)(225,274)(226,273)(227,272)
(228,271)(229,279)(230,278)(231,277)(232,282)(233,281)(234,280)(235,288)
(236,287)(237,286)(238,285)(239,284)(240,283)(289,369)(290,368)(291,367)
(292,372)(293,371)(294,370)(295,366)(296,365)(297,364)(298,363)(299,362)
(300,361)(301,381)(302,380)(303,379)(304,384)(305,383)(306,382)(307,378)
(308,377)(309,376)(310,375)(311,374)(312,373)(313,345)(314,344)(315,343)
(316,348)(317,347)(318,346)(319,342)(320,341)(321,340)(322,339)(323,338)
(324,337)(325,357)(326,356)(327,355)(328,360)(329,359)(330,358)(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)( 25,121)( 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,
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