Polytope of Type {24,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,16}*768e
if this polytope has a name.
Group : SmallGroup(768,83049)
Rank : 3
Schlafli Type : {24,16}
Number of vertices, edges, etc : 24, 192, 16
Order of s0s1s2 : 48
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {24,8}*384d, {12,16}*384b
3-fold quotients : {8,16}*256e
4-fold quotients : {24,4}*192b, {12,8}*192a
6-fold quotients : {8,8}*128a, {4,16}*128b
8-fold quotients : {12,4}*96a, {6,8}*96
12-fold quotients : {4,8}*64a, {8,4}*64b
16-fold quotients : {12,2}*48, {6,4}*48a
24-fold quotients : {4,4}*32, {2,8}*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, 97)( 2, 99)( 3, 98)( 4,100)( 5,102)( 6,101)( 7,103)( 8,105)
( 9,104)( 10,106)( 11,108)( 12,107)( 13,109)( 14,111)( 15,110)( 16,112)
( 17,114)( 18,113)( 19,115)( 20,117)( 21,116)( 22,118)( 23,120)( 24,119)
( 25,130)( 26,132)( 27,131)( 28,127)( 29,129)( 30,128)( 31,124)( 32,126)
( 33,125)( 34,121)( 35,123)( 36,122)( 37,142)( 38,144)( 39,143)( 40,139)
( 41,141)( 42,140)( 43,136)( 44,138)( 45,137)( 46,133)( 47,135)( 48,134)
( 49,151)( 50,153)( 51,152)( 52,154)( 53,156)( 54,155)( 55,145)( 56,147)
( 57,146)( 58,148)( 59,150)( 60,149)( 61,163)( 62,165)( 63,164)( 64,166)
( 65,168)( 66,167)( 67,157)( 68,159)( 69,158)( 70,160)( 71,162)( 72,161)
( 73,172)( 74,174)( 75,173)( 76,169)( 77,171)( 78,170)( 79,178)( 80,180)
( 81,179)( 82,175)( 83,177)( 84,176)( 85,184)( 86,186)( 87,185)( 88,181)
( 89,183)( 90,182)( 91,190)( 92,192)( 93,191)( 94,187)( 95,189)( 96,188)
(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,295)(200,297)
(201,296)(202,298)(203,300)(204,299)(205,301)(206,303)(207,302)(208,304)
(209,306)(210,305)(211,307)(212,309)(213,308)(214,310)(215,312)(216,311)
(217,322)(218,324)(219,323)(220,319)(221,321)(222,320)(223,316)(224,318)
(225,317)(226,313)(227,315)(228,314)(229,334)(230,336)(231,335)(232,331)
(233,333)(234,332)(235,328)(236,330)(237,329)(238,325)(239,327)(240,326)
(241,343)(242,345)(243,344)(244,346)(245,348)(246,347)(247,337)(248,339)
(249,338)(250,340)(251,342)(252,341)(253,355)(254,357)(255,356)(256,358)
(257,360)(258,359)(259,349)(260,351)(261,350)(262,352)(263,354)(264,353)
(265,364)(266,366)(267,365)(268,361)(269,363)(270,362)(271,370)(272,372)
(273,371)(274,367)(275,369)(276,368)(277,376)(278,378)(279,377)(280,373)
(281,375)(282,374)(283,382)(284,384)(285,383)(286,379)(287,381)(288,380);;
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 := ( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,199)( 8,200)
( 9,201)( 10,202)( 11,203)( 12,204)( 13,208)( 14,209)( 15,210)( 16,205)
( 17,206)( 18,207)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)( 24,213)
( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,217)( 32,218)
( 33,219)( 34,220)( 35,221)( 36,222)( 37,238)( 38,239)( 39,240)( 40,235)
( 41,236)( 42,237)( 43,232)( 44,233)( 45,234)( 46,229)( 47,230)( 48,231)
( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,259)( 56,260)
( 57,261)( 58,262)( 59,263)( 60,264)( 61,241)( 62,242)( 63,243)( 64,244)
( 65,245)( 66,246)( 67,247)( 68,248)( 69,249)( 70,250)( 71,251)( 72,252)
( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,277)( 80,278)
( 81,279)( 82,280)( 83,281)( 84,282)( 85,271)( 86,272)( 87,273)( 88,274)
( 89,275)( 90,276)( 91,265)( 92,266)( 93,267)( 94,268)( 95,269)( 96,270)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,295)(104,296)
(105,297)(106,298)(107,299)(108,300)(109,304)(110,305)(111,306)(112,301)
(113,302)(114,303)(115,310)(116,311)(117,312)(118,307)(119,308)(120,309)
(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,313)(128,314)
(129,315)(130,316)(131,317)(132,318)(133,334)(134,335)(135,336)(136,331)
(137,332)(138,333)(139,328)(140,329)(141,330)(142,325)(143,326)(144,327)
(145,349)(146,350)(147,351)(148,352)(149,353)(150,354)(151,355)(152,356)
(153,357)(154,358)(155,359)(156,360)(157,337)(158,338)(159,339)(160,340)
(161,341)(162,342)(163,343)(164,344)(165,345)(166,346)(167,347)(168,348)
(169,379)(170,380)(171,381)(172,382)(173,383)(174,384)(175,373)(176,374)
(177,375)(178,376)(179,377)(180,378)(181,367)(182,368)(183,369)(184,370)
(185,371)(186,372)(187,361)(188,362)(189,363)(190,364)(191,365)(192,366);;
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,
s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1, 97)( 2, 99)( 3, 98)( 4,100)( 5,102)( 6,101)( 7,103)
( 8,105)( 9,104)( 10,106)( 11,108)( 12,107)( 13,109)( 14,111)( 15,110)
( 16,112)( 17,114)( 18,113)( 19,115)( 20,117)( 21,116)( 22,118)( 23,120)
( 24,119)( 25,130)( 26,132)( 27,131)( 28,127)( 29,129)( 30,128)( 31,124)
( 32,126)( 33,125)( 34,121)( 35,123)( 36,122)( 37,142)( 38,144)( 39,143)
( 40,139)( 41,141)( 42,140)( 43,136)( 44,138)( 45,137)( 46,133)( 47,135)
( 48,134)( 49,151)( 50,153)( 51,152)( 52,154)( 53,156)( 54,155)( 55,145)
( 56,147)( 57,146)( 58,148)( 59,150)( 60,149)( 61,163)( 62,165)( 63,164)
( 64,166)( 65,168)( 66,167)( 67,157)( 68,159)( 69,158)( 70,160)( 71,162)
( 72,161)( 73,172)( 74,174)( 75,173)( 76,169)( 77,171)( 78,170)( 79,178)
( 80,180)( 81,179)( 82,175)( 83,177)( 84,176)( 85,184)( 86,186)( 87,185)
( 88,181)( 89,183)( 90,182)( 91,190)( 92,192)( 93,191)( 94,187)( 95,189)
( 96,188)(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,295)
(200,297)(201,296)(202,298)(203,300)(204,299)(205,301)(206,303)(207,302)
(208,304)(209,306)(210,305)(211,307)(212,309)(213,308)(214,310)(215,312)
(216,311)(217,322)(218,324)(219,323)(220,319)(221,321)(222,320)(223,316)
(224,318)(225,317)(226,313)(227,315)(228,314)(229,334)(230,336)(231,335)
(232,331)(233,333)(234,332)(235,328)(236,330)(237,329)(238,325)(239,327)
(240,326)(241,343)(242,345)(243,344)(244,346)(245,348)(246,347)(247,337)
(248,339)(249,338)(250,340)(251,342)(252,341)(253,355)(254,357)(255,356)
(256,358)(257,360)(258,359)(259,349)(260,351)(261,350)(262,352)(263,354)
(264,353)(265,364)(266,366)(267,365)(268,361)(269,363)(270,362)(271,370)
(272,372)(273,371)(274,367)(275,369)(276,368)(277,376)(278,378)(279,377)
(280,373)(281,375)(282,374)(283,382)(284,384)(285,383)(286,379)(287,381)
(288,380);
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)!( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,199)
( 8,200)( 9,201)( 10,202)( 11,203)( 12,204)( 13,208)( 14,209)( 15,210)
( 16,205)( 17,206)( 18,207)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)
( 24,213)( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,217)
( 32,218)( 33,219)( 34,220)( 35,221)( 36,222)( 37,238)( 38,239)( 39,240)
( 40,235)( 41,236)( 42,237)( 43,232)( 44,233)( 45,234)( 46,229)( 47,230)
( 48,231)( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,259)
( 56,260)( 57,261)( 58,262)( 59,263)( 60,264)( 61,241)( 62,242)( 63,243)
( 64,244)( 65,245)( 66,246)( 67,247)( 68,248)( 69,249)( 70,250)( 71,251)
( 72,252)( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,277)
( 80,278)( 81,279)( 82,280)( 83,281)( 84,282)( 85,271)( 86,272)( 87,273)
( 88,274)( 89,275)( 90,276)( 91,265)( 92,266)( 93,267)( 94,268)( 95,269)
( 96,270)( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,295)
(104,296)(105,297)(106,298)(107,299)(108,300)(109,304)(110,305)(111,306)
(112,301)(113,302)(114,303)(115,310)(116,311)(117,312)(118,307)(119,308)
(120,309)(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,313)
(128,314)(129,315)(130,316)(131,317)(132,318)(133,334)(134,335)(135,336)
(136,331)(137,332)(138,333)(139,328)(140,329)(141,330)(142,325)(143,326)
(144,327)(145,349)(146,350)(147,351)(148,352)(149,353)(150,354)(151,355)
(152,356)(153,357)(154,358)(155,359)(156,360)(157,337)(158,338)(159,339)
(160,340)(161,341)(162,342)(163,343)(164,344)(165,345)(166,346)(167,347)
(168,348)(169,379)(170,380)(171,381)(172,382)(173,383)(174,384)(175,373)
(176,374)(177,375)(178,376)(179,377)(180,378)(181,367)(182,368)(183,369)
(184,370)(185,371)(186,372)(187,361)(188,362)(189,363)(190,364)(191,365)
(192,366);
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,
s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0 >;
References : None.
to this polytope