Polytope of Type {24,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,16}*768d
Also Known As : {24,16|2}. if this polytope has another name.
Group : SmallGroup(768,82995)
Rank : 3
Schlafli Type : {24,16}
Number of vertices, edges, etc : 24, 192, 16
Order of s0s1s2 : 48
Order of s0s1s2s1 : 2
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}*384b, {12,16}*384a
3-fold quotients : {8,16}*256d
4-fold quotients : {24,4}*192a, {12,8}*192a, {6,16}*192
6-fold quotients : {8,8}*128b, {4,16}*128a
8-fold quotients : {12,4}*96a, {24,2}*96, {6,8}*96
12-fold quotients : {4,8}*64a, {8,4}*64a, {2,16}*64
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, 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)
( 25,127)( 26,129)( 27,128)( 28,130)( 29,132)( 30,131)( 31,121)( 32,123)
( 33,122)( 34,124)( 35,126)( 36,125)( 37,139)( 38,141)( 39,140)( 40,142)
( 41,144)( 42,143)( 43,133)( 44,135)( 45,134)( 46,136)( 47,138)( 48,137)
( 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)
( 73,169)( 74,171)( 75,170)( 76,172)( 77,174)( 78,173)( 79,175)( 80,177)
( 81,176)( 82,178)( 83,180)( 84,179)( 85,181)( 86,183)( 87,182)( 88,184)
( 89,186)( 90,185)( 91,187)( 92,189)( 93,188)( 94,190)( 95,192)( 96,191)
(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)
(217,319)(218,321)(219,320)(220,322)(221,324)(222,323)(223,313)(224,315)
(225,314)(226,316)(227,318)(228,317)(229,331)(230,333)(231,332)(232,334)
(233,336)(234,335)(235,325)(236,327)(237,326)(238,328)(239,330)(240,329)
(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)
(265,361)(266,363)(267,362)(268,364)(269,366)(270,365)(271,367)(272,369)
(273,368)(274,370)(275,372)(276,371)(277,373)(278,375)(279,374)(280,376)
(281,378)(282,377)(283,379)(284,381)(285,380)(286,382)(287,384)(288,383);;
s1 := ( 1, 3)( 4, 6)( 7, 9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)( 19, 24)
( 20, 23)( 21, 22)( 25, 33)( 26, 32)( 27, 31)( 28, 36)( 29, 35)( 30, 34)
( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 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, 93)( 74, 92)( 75, 91)( 76, 96)( 77, 95)( 78, 94)
( 79, 87)( 80, 86)( 81, 85)( 82, 90)( 83, 89)( 84, 88)( 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)(217,273)(218,272)
(219,271)(220,276)(221,275)(222,274)(223,267)(224,266)(225,265)(226,270)
(227,269)(228,268)(229,288)(230,287)(231,286)(232,285)(233,284)(234,283)
(235,282)(236,281)(237,280)(238,279)(239,278)(240,277)(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 := ( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)( 8,296)
( 9,297)( 10,298)( 11,299)( 12,300)( 13,304)( 14,305)( 15,306)( 16,301)
( 17,302)( 18,303)( 19,310)( 20,311)( 21,312)( 22,307)( 23,308)( 24,309)
( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)
( 33,321)( 34,322)( 35,323)( 36,324)( 37,328)( 38,329)( 39,330)( 40,325)
( 41,326)( 42,327)( 43,334)( 44,335)( 45,336)( 46,331)( 47,332)( 48,333)
( 49,355)( 50,356)( 51,357)( 52,358)( 53,359)( 54,360)( 55,349)( 56,350)
( 57,351)( 58,352)( 59,353)( 60,354)( 61,343)( 62,344)( 63,345)( 64,346)
( 65,347)( 66,348)( 67,337)( 68,338)( 69,339)( 70,340)( 71,341)( 72,342)
( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,373)( 80,374)
( 81,375)( 82,376)( 83,377)( 84,378)( 85,367)( 86,368)( 87,369)( 88,370)
( 89,371)( 90,372)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)( 96,366)
( 97,193)( 98,194)( 99,195)(100,196)(101,197)(102,198)(103,199)(104,200)
(105,201)(106,202)(107,203)(108,204)(109,208)(110,209)(111,210)(112,205)
(113,206)(114,207)(115,214)(116,215)(117,216)(118,211)(119,212)(120,213)
(121,217)(122,218)(123,219)(124,220)(125,221)(126,222)(127,223)(128,224)
(129,225)(130,226)(131,227)(132,228)(133,232)(134,233)(135,234)(136,229)
(137,230)(138,231)(139,238)(140,239)(141,240)(142,235)(143,236)(144,237)
(145,259)(146,260)(147,261)(148,262)(149,263)(150,264)(151,253)(152,254)
(153,255)(154,256)(155,257)(156,258)(157,247)(158,248)(159,249)(160,250)
(161,251)(162,252)(163,241)(164,242)(165,243)(166,244)(167,245)(168,246)
(169,283)(170,284)(171,285)(172,286)(173,287)(174,288)(175,277)(176,278)
(177,279)(178,280)(179,281)(180,282)(181,271)(182,272)(183,273)(184,274)
(185,275)(186,276)(187,265)(188,266)(189,267)(190,268)(191,269)(192,270);;
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*s2*s1*s0*s1*s2*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,
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, 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)( 25,127)( 26,129)( 27,128)( 28,130)( 29,132)( 30,131)( 31,121)
( 32,123)( 33,122)( 34,124)( 35,126)( 36,125)( 37,139)( 38,141)( 39,140)
( 40,142)( 41,144)( 42,143)( 43,133)( 44,135)( 45,134)( 46,136)( 47,138)
( 48,137)( 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)( 73,169)( 74,171)( 75,170)( 76,172)( 77,174)( 78,173)( 79,175)
( 80,177)( 81,176)( 82,178)( 83,180)( 84,179)( 85,181)( 86,183)( 87,182)
( 88,184)( 89,186)( 90,185)( 91,187)( 92,189)( 93,188)( 94,190)( 95,192)
( 96,191)(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)(217,319)(218,321)(219,320)(220,322)(221,324)(222,323)(223,313)
(224,315)(225,314)(226,316)(227,318)(228,317)(229,331)(230,333)(231,332)
(232,334)(233,336)(234,335)(235,325)(236,327)(237,326)(238,328)(239,330)
(240,329)(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)(265,361)(266,363)(267,362)(268,364)(269,366)(270,365)(271,367)
(272,369)(273,368)(274,370)(275,372)(276,371)(277,373)(278,375)(279,374)
(280,376)(281,378)(282,377)(283,379)(284,381)(285,380)(286,382)(287,384)
(288,383);
s1 := Sym(384)!( 1, 3)( 4, 6)( 7, 9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)
( 19, 24)( 20, 23)( 21, 22)( 25, 33)( 26, 32)( 27, 31)( 28, 36)( 29, 35)
( 30, 34)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 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, 93)( 74, 92)( 75, 91)( 76, 96)( 77, 95)
( 78, 94)( 79, 87)( 80, 86)( 81, 85)( 82, 90)( 83, 89)( 84, 88)( 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)(217,273)
(218,272)(219,271)(220,276)(221,275)(222,274)(223,267)(224,266)(225,265)
(226,270)(227,269)(228,268)(229,288)(230,287)(231,286)(232,285)(233,284)
(234,283)(235,282)(236,281)(237,280)(238,279)(239,278)(240,277)(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)!( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)
( 8,296)( 9,297)( 10,298)( 11,299)( 12,300)( 13,304)( 14,305)( 15,306)
( 16,301)( 17,302)( 18,303)( 19,310)( 20,311)( 21,312)( 22,307)( 23,308)
( 24,309)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)
( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 37,328)( 38,329)( 39,330)
( 40,325)( 41,326)( 42,327)( 43,334)( 44,335)( 45,336)( 46,331)( 47,332)
( 48,333)( 49,355)( 50,356)( 51,357)( 52,358)( 53,359)( 54,360)( 55,349)
( 56,350)( 57,351)( 58,352)( 59,353)( 60,354)( 61,343)( 62,344)( 63,345)
( 64,346)( 65,347)( 66,348)( 67,337)( 68,338)( 69,339)( 70,340)( 71,341)
( 72,342)( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,373)
( 80,374)( 81,375)( 82,376)( 83,377)( 84,378)( 85,367)( 86,368)( 87,369)
( 88,370)( 89,371)( 90,372)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)
( 96,366)( 97,193)( 98,194)( 99,195)(100,196)(101,197)(102,198)(103,199)
(104,200)(105,201)(106,202)(107,203)(108,204)(109,208)(110,209)(111,210)
(112,205)(113,206)(114,207)(115,214)(116,215)(117,216)(118,211)(119,212)
(120,213)(121,217)(122,218)(123,219)(124,220)(125,221)(126,222)(127,223)
(128,224)(129,225)(130,226)(131,227)(132,228)(133,232)(134,233)(135,234)
(136,229)(137,230)(138,231)(139,238)(140,239)(141,240)(142,235)(143,236)
(144,237)(145,259)(146,260)(147,261)(148,262)(149,263)(150,264)(151,253)
(152,254)(153,255)(154,256)(155,257)(156,258)(157,247)(158,248)(159,249)
(160,250)(161,251)(162,252)(163,241)(164,242)(165,243)(166,244)(167,245)
(168,246)(169,283)(170,284)(171,285)(172,286)(173,287)(174,288)(175,277)
(176,278)(177,279)(178,280)(179,281)(180,282)(181,271)(182,272)(183,273)
(184,274)(185,275)(186,276)(187,265)(188,266)(189,267)(190,268)(191,269)
(192,270);
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*s2*s1*s0*s1*s2*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,
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