Polytope of Type {16,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,24}*768f
if this polytope has a name.
Group : SmallGroup(768,83051)
Rank : 3
Schlafli Type : {16,24}
Number of vertices, edges, etc : 16, 192, 24
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 : {8,24}*384b, {16,12}*384b
   3-fold quotients : {16,8}*256f
   4-fold quotients : {4,24}*192a, {8,12}*192a
   6-fold quotients : {8,8}*128b, {16,4}*128b
   8-fold quotients : {4,12}*96a, {2,24}*96, {8,6}*96
   12-fold quotients : {4,8}*64a, {8,4}*64a
   16-fold quotients : {2,12}*48, {4,6}*48a
   24-fold quotients : {4,4}*32, {2,8}*32, {8,2}*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 := (  1,289)(  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)
( 25,316)( 26,317)( 27,318)( 28,313)( 29,314)( 30,315)( 31,322)( 32,323)
( 33,324)( 34,319)( 35,320)( 36,321)( 37,325)( 38,326)( 39,327)( 40,328)
( 41,329)( 42,330)( 43,331)( 44,332)( 45,333)( 46,334)( 47,335)( 48,336)
( 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)
( 73,382)( 74,383)( 75,384)( 76,379)( 77,380)( 78,381)( 79,376)( 80,377)
( 81,378)( 82,373)( 83,374)( 84,375)( 85,370)( 86,371)( 87,372)( 88,367)
( 89,368)( 90,369)( 91,364)( 92,365)( 93,366)( 94,361)( 95,362)( 96,363)
( 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)
(121,220)(122,221)(123,222)(124,217)(125,218)(126,219)(127,226)(128,227)
(129,228)(130,223)(131,224)(132,225)(133,229)(134,230)(135,231)(136,232)
(137,233)(138,234)(139,235)(140,236)(141,237)(142,238)(143,239)(144,240)
(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)
(169,286)(170,287)(171,288)(172,283)(173,284)(174,285)(175,280)(176,281)
(177,282)(178,277)(179,278)(180,279)(181,274)(182,275)(183,276)(184,271)
(185,272)(186,273)(187,268)(188,269)(189,270)(190,265)(191,266)(192,267);;
s1 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 19, 22)
( 20, 24)( 21, 23)( 25, 34)( 26, 36)( 27, 35)( 28, 31)( 29, 33)( 30, 32)
( 37, 43)( 38, 45)( 39, 44)( 40, 46)( 41, 48)( 42, 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, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)
( 79, 88)( 80, 90)( 81, 89)( 82, 85)( 83, 87)( 84, 86)( 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)(217,274)(218,276)
(219,275)(220,271)(221,273)(222,272)(223,268)(224,270)(225,269)(226,265)
(227,267)(228,266)(229,283)(230,285)(231,284)(232,286)(233,288)(234,287)
(235,277)(236,279)(237,278)(238,280)(239,282)(240,281)(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, 99)(  2, 98)(  3, 97)(  4,102)(  5,101)(  6,100)(  7,105)(  8,104)
(  9,103)( 10,108)( 11,107)( 12,106)( 13,111)( 14,110)( 15,109)( 16,114)
( 17,113)( 18,112)( 19,117)( 20,116)( 21,115)( 22,120)( 23,119)( 24,118)
( 25,132)( 26,131)( 27,130)( 28,129)( 29,128)( 30,127)( 31,126)( 32,125)
( 33,124)( 34,123)( 35,122)( 36,121)( 37,144)( 38,143)( 39,142)( 40,141)
( 41,140)( 42,139)( 43,138)( 44,137)( 45,136)( 46,135)( 47,134)( 48,133)
( 49,153)( 50,152)( 51,151)( 52,156)( 53,155)( 54,154)( 55,147)( 56,146)
( 57,145)( 58,150)( 59,149)( 60,148)( 61,165)( 62,164)( 63,163)( 64,168)
( 65,167)( 66,166)( 67,159)( 68,158)( 69,157)( 70,162)( 71,161)( 72,160)
( 73,174)( 74,173)( 75,172)( 76,171)( 77,170)( 78,169)( 79,180)( 80,179)
( 81,178)( 82,177)( 83,176)( 84,175)( 85,186)( 86,185)( 87,184)( 88,183)
( 89,182)( 90,181)( 91,192)( 92,191)( 93,190)( 94,189)( 95,188)( 96,187)
(193,291)(194,290)(195,289)(196,294)(197,293)(198,292)(199,297)(200,296)
(201,295)(202,300)(203,299)(204,298)(205,303)(206,302)(207,301)(208,306)
(209,305)(210,304)(211,309)(212,308)(213,307)(214,312)(215,311)(216,310)
(217,324)(218,323)(219,322)(220,321)(221,320)(222,319)(223,318)(224,317)
(225,316)(226,315)(227,314)(228,313)(229,336)(230,335)(231,334)(232,333)
(233,332)(234,331)(235,330)(236,329)(237,328)(238,327)(239,326)(240,325)
(241,345)(242,344)(243,343)(244,348)(245,347)(246,346)(247,339)(248,338)
(249,337)(250,342)(251,341)(252,340)(253,357)(254,356)(255,355)(256,360)
(257,359)(258,358)(259,351)(260,350)(261,349)(262,354)(263,353)(264,352)
(265,366)(266,365)(267,364)(268,363)(269,362)(270,361)(271,372)(272,371)
(273,370)(274,369)(275,368)(276,367)(277,378)(278,377)(279,376)(280,375)
(281,374)(282,373)(283,384)(284,383)(285,382)(286,381)(287,380)(288,379);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*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)!(  1,289)(  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)( 25,316)( 26,317)( 27,318)( 28,313)( 29,314)( 30,315)( 31,322)
( 32,323)( 33,324)( 34,319)( 35,320)( 36,321)( 37,325)( 38,326)( 39,327)
( 40,328)( 41,329)( 42,330)( 43,331)( 44,332)( 45,333)( 46,334)( 47,335)
( 48,336)( 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)( 73,382)( 74,383)( 75,384)( 76,379)( 77,380)( 78,381)( 79,376)
( 80,377)( 81,378)( 82,373)( 83,374)( 84,375)( 85,370)( 86,371)( 87,372)
( 88,367)( 89,368)( 90,369)( 91,364)( 92,365)( 93,366)( 94,361)( 95,362)
( 96,363)( 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)(121,220)(122,221)(123,222)(124,217)(125,218)(126,219)(127,226)
(128,227)(129,228)(130,223)(131,224)(132,225)(133,229)(134,230)(135,231)
(136,232)(137,233)(138,234)(139,235)(140,236)(141,237)(142,238)(143,239)
(144,240)(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)(169,286)(170,287)(171,288)(172,283)(173,284)(174,285)(175,280)
(176,281)(177,282)(178,277)(179,278)(180,279)(181,274)(182,275)(183,276)
(184,271)(185,272)(186,273)(187,268)(188,269)(189,270)(190,265)(191,266)
(192,267);
s1 := Sym(384)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 19, 22)( 20, 24)( 21, 23)( 25, 34)( 26, 36)( 27, 35)( 28, 31)( 29, 33)
( 30, 32)( 37, 43)( 38, 45)( 39, 44)( 40, 46)( 41, 48)( 42, 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, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)
( 78, 92)( 79, 88)( 80, 90)( 81, 89)( 82, 85)( 83, 87)( 84, 86)( 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)(217,274)
(218,276)(219,275)(220,271)(221,273)(222,272)(223,268)(224,270)(225,269)
(226,265)(227,267)(228,266)(229,283)(230,285)(231,284)(232,286)(233,288)
(234,287)(235,277)(236,279)(237,278)(238,280)(239,282)(240,281)(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, 99)(  2, 98)(  3, 97)(  4,102)(  5,101)(  6,100)(  7,105)
(  8,104)(  9,103)( 10,108)( 11,107)( 12,106)( 13,111)( 14,110)( 15,109)
( 16,114)( 17,113)( 18,112)( 19,117)( 20,116)( 21,115)( 22,120)( 23,119)
( 24,118)( 25,132)( 26,131)( 27,130)( 28,129)( 29,128)( 30,127)( 31,126)
( 32,125)( 33,124)( 34,123)( 35,122)( 36,121)( 37,144)( 38,143)( 39,142)
( 40,141)( 41,140)( 42,139)( 43,138)( 44,137)( 45,136)( 46,135)( 47,134)
( 48,133)( 49,153)( 50,152)( 51,151)( 52,156)( 53,155)( 54,154)( 55,147)
( 56,146)( 57,145)( 58,150)( 59,149)( 60,148)( 61,165)( 62,164)( 63,163)
( 64,168)( 65,167)( 66,166)( 67,159)( 68,158)( 69,157)( 70,162)( 71,161)
( 72,160)( 73,174)( 74,173)( 75,172)( 76,171)( 77,170)( 78,169)( 79,180)
( 80,179)( 81,178)( 82,177)( 83,176)( 84,175)( 85,186)( 86,185)( 87,184)
( 88,183)( 89,182)( 90,181)( 91,192)( 92,191)( 93,190)( 94,189)( 95,188)
( 96,187)(193,291)(194,290)(195,289)(196,294)(197,293)(198,292)(199,297)
(200,296)(201,295)(202,300)(203,299)(204,298)(205,303)(206,302)(207,301)
(208,306)(209,305)(210,304)(211,309)(212,308)(213,307)(214,312)(215,311)
(216,310)(217,324)(218,323)(219,322)(220,321)(221,320)(222,319)(223,318)
(224,317)(225,316)(226,315)(227,314)(228,313)(229,336)(230,335)(231,334)
(232,333)(233,332)(234,331)(235,330)(236,329)(237,328)(238,327)(239,326)
(240,325)(241,345)(242,344)(243,343)(244,348)(245,347)(246,346)(247,339)
(248,338)(249,337)(250,342)(251,341)(252,340)(253,357)(254,356)(255,355)
(256,360)(257,359)(258,358)(259,351)(260,350)(261,349)(262,354)(263,353)
(264,352)(265,366)(266,365)(267,364)(268,363)(269,362)(270,361)(271,372)
(272,371)(273,370)(274,369)(275,368)(276,367)(277,378)(278,377)(279,376)
(280,375)(281,374)(282,373)(283,384)(284,383)(285,382)(286,381)(287,380)
(288,379);
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*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