Polytope of Type {16,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,12}*768b
if this polytope has a name.
Group : SmallGroup(768,81734)
Rank : 3
Schlafli Type : {16,12}
Number of vertices, edges, etc : 32, 192, 24
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 : {8,12}*384a
3-fold quotients : {16,4}*256b
4-fold quotients : {4,12}*192a, {8,12}*192a, {8,12}*192b
6-fold quotients : {8,4}*128a
8-fold quotients : {4,12}*96a, {8,6}*96
12-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
16-fold quotients : {2,12}*48, {4,6}*48a
24-fold quotients : {4,4}*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 := ( 1,193)( 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)
( 25,226)( 26,227)( 27,228)( 28,223)( 29,224)( 30,225)( 31,220)( 32,221)
( 33,222)( 34,217)( 35,218)( 36,219)( 37,235)( 38,236)( 39,237)( 40,238)
( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)( 48,234)
( 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)
( 73,286)( 74,287)( 75,288)( 76,283)( 77,284)( 78,285)( 79,280)( 80,281)
( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)( 88,271)
( 89,272)( 90,273)( 91,268)( 92,269)( 93,270)( 94,265)( 95,266)( 96,267)
( 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)
(121,322)(122,323)(123,324)(124,319)(125,320)(126,321)(127,316)(128,317)
(129,318)(130,313)(131,314)(132,315)(133,331)(134,332)(135,333)(136,334)
(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)(144,330)
(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)
(169,382)(170,383)(171,384)(172,379)(173,380)(174,381)(175,376)(176,377)
(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)(184,367)
(185,368)(186,369)(187,364)(188,365)(189,366)(190,361)(191,362)(192,363);;
s1 := ( 2, 3)( 5, 6)( 7, 10)( 8, 12)( 9, 11)( 13, 16)( 14, 18)( 15, 17)
( 20, 21)( 23, 24)( 26, 27)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 37, 40)
( 38, 42)( 39, 41)( 44, 45)( 47, 48)( 49, 61)( 50, 63)( 51, 62)( 52, 64)
( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)( 58, 67)( 59, 69)( 60, 68)
( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)( 78, 89)( 79, 94)( 80, 96)
( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)( 98,123)( 99,122)(100,124)
(101,126)(102,125)(103,130)(104,132)(105,131)(106,127)(107,129)(108,128)
(109,136)(110,138)(111,137)(112,133)(113,135)(114,134)(115,139)(116,141)
(117,140)(118,142)(119,144)(120,143)(145,184)(146,186)(147,185)(148,181)
(149,183)(150,182)(151,187)(152,189)(153,188)(154,190)(155,192)(156,191)
(157,172)(158,174)(159,173)(160,169)(161,171)(162,170)(163,175)(164,177)
(165,176)(166,178)(167,180)(168,179)(193,241)(194,243)(195,242)(196,244)
(197,246)(198,245)(199,250)(200,252)(201,251)(202,247)(203,249)(204,248)
(205,256)(206,258)(207,257)(208,253)(209,255)(210,254)(211,259)(212,261)
(213,260)(214,262)(215,264)(216,263)(217,265)(218,267)(219,266)(220,268)
(221,270)(222,269)(223,274)(224,276)(225,275)(226,271)(227,273)(228,272)
(229,280)(230,282)(231,281)(232,277)(233,279)(234,278)(235,283)(236,285)
(237,284)(238,286)(239,288)(240,287)(289,367)(290,369)(291,368)(292,370)
(293,372)(294,371)(295,364)(296,366)(297,365)(298,361)(299,363)(300,362)
(301,382)(302,384)(303,383)(304,379)(305,381)(306,380)(307,373)(308,375)
(309,374)(310,376)(311,378)(312,377)(313,343)(314,345)(315,344)(316,346)
(317,348)(318,347)(319,340)(320,342)(321,341)(322,337)(323,339)(324,338)
(325,358)(326,360)(327,359)(328,355)(329,357)(330,356)(331,349)(332,351)
(333,350)(334,352)(335,354)(336,353);;
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)
( 25,123)( 26,122)( 27,121)( 28,126)( 29,125)( 30,124)( 31,129)( 32,128)
( 33,127)( 34,132)( 35,131)( 36,130)( 37,135)( 38,134)( 39,133)( 40,138)
( 41,137)( 42,136)( 43,141)( 44,140)( 45,139)( 46,144)( 47,143)( 48,142)
( 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)
( 73,177)( 74,176)( 75,175)( 76,180)( 77,179)( 78,178)( 79,171)( 80,170)
( 81,169)( 82,174)( 83,173)( 84,172)( 85,189)( 86,188)( 87,187)( 88,192)
( 89,191)( 90,190)( 91,183)( 92,182)( 93,181)( 94,186)( 95,185)( 96,184)
(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)
(217,315)(218,314)(219,313)(220,318)(221,317)(222,316)(223,321)(224,320)
(225,319)(226,324)(227,323)(228,322)(229,327)(230,326)(231,325)(232,330)
(233,329)(234,328)(235,333)(236,332)(237,331)(238,336)(239,335)(240,334)
(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)
(265,369)(266,368)(267,367)(268,372)(269,371)(270,370)(271,363)(272,362)
(273,361)(274,366)(275,365)(276,364)(277,381)(278,380)(279,379)(280,384)
(281,383)(282,382)(283,375)(284,374)(285,373)(286,378)(287,377)(288,376);;
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*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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 25,226)( 26,227)( 27,228)( 28,223)( 29,224)( 30,225)( 31,220)
( 32,221)( 33,222)( 34,217)( 35,218)( 36,219)( 37,235)( 38,236)( 39,237)
( 40,238)( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)
( 48,234)( 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)( 73,286)( 74,287)( 75,288)( 76,283)( 77,284)( 78,285)( 79,280)
( 80,281)( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)
( 88,271)( 89,272)( 90,273)( 91,268)( 92,269)( 93,270)( 94,265)( 95,266)
( 96,267)( 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)(121,322)(122,323)(123,324)(124,319)(125,320)(126,321)(127,316)
(128,317)(129,318)(130,313)(131,314)(132,315)(133,331)(134,332)(135,333)
(136,334)(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)
(144,330)(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)(169,382)(170,383)(171,384)(172,379)(173,380)(174,381)(175,376)
(176,377)(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)
(184,367)(185,368)(186,369)(187,364)(188,365)(189,366)(190,361)(191,362)
(192,363);
s1 := Sym(384)!( 2, 3)( 5, 6)( 7, 10)( 8, 12)( 9, 11)( 13, 16)( 14, 18)
( 15, 17)( 20, 21)( 23, 24)( 26, 27)( 29, 30)( 31, 34)( 32, 36)( 33, 35)
( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 47, 48)( 49, 61)( 50, 63)( 51, 62)
( 52, 64)( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)( 58, 67)( 59, 69)
( 60, 68)( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)( 78, 89)( 79, 94)
( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)( 98,123)( 99,122)
(100,124)(101,126)(102,125)(103,130)(104,132)(105,131)(106,127)(107,129)
(108,128)(109,136)(110,138)(111,137)(112,133)(113,135)(114,134)(115,139)
(116,141)(117,140)(118,142)(119,144)(120,143)(145,184)(146,186)(147,185)
(148,181)(149,183)(150,182)(151,187)(152,189)(153,188)(154,190)(155,192)
(156,191)(157,172)(158,174)(159,173)(160,169)(161,171)(162,170)(163,175)
(164,177)(165,176)(166,178)(167,180)(168,179)(193,241)(194,243)(195,242)
(196,244)(197,246)(198,245)(199,250)(200,252)(201,251)(202,247)(203,249)
(204,248)(205,256)(206,258)(207,257)(208,253)(209,255)(210,254)(211,259)
(212,261)(213,260)(214,262)(215,264)(216,263)(217,265)(218,267)(219,266)
(220,268)(221,270)(222,269)(223,274)(224,276)(225,275)(226,271)(227,273)
(228,272)(229,280)(230,282)(231,281)(232,277)(233,279)(234,278)(235,283)
(236,285)(237,284)(238,286)(239,288)(240,287)(289,367)(290,369)(291,368)
(292,370)(293,372)(294,371)(295,364)(296,366)(297,365)(298,361)(299,363)
(300,362)(301,382)(302,384)(303,383)(304,379)(305,381)(306,380)(307,373)
(308,375)(309,374)(310,376)(311,378)(312,377)(313,343)(314,345)(315,344)
(316,346)(317,348)(318,347)(319,340)(320,342)(321,341)(322,337)(323,339)
(324,338)(325,358)(326,360)(327,359)(328,355)(329,357)(330,356)(331,349)
(332,351)(333,350)(334,352)(335,354)(336,353);
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)( 25,123)( 26,122)( 27,121)( 28,126)( 29,125)( 30,124)( 31,129)
( 32,128)( 33,127)( 34,132)( 35,131)( 36,130)( 37,135)( 38,134)( 39,133)
( 40,138)( 41,137)( 42,136)( 43,141)( 44,140)( 45,139)( 46,144)( 47,143)
( 48,142)( 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)( 73,177)( 74,176)( 75,175)( 76,180)( 77,179)( 78,178)( 79,171)
( 80,170)( 81,169)( 82,174)( 83,173)( 84,172)( 85,189)( 86,188)( 87,187)
( 88,192)( 89,191)( 90,190)( 91,183)( 92,182)( 93,181)( 94,186)( 95,185)
( 96,184)(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)(217,315)(218,314)(219,313)(220,318)(221,317)(222,316)(223,321)
(224,320)(225,319)(226,324)(227,323)(228,322)(229,327)(230,326)(231,325)
(232,330)(233,329)(234,328)(235,333)(236,332)(237,331)(238,336)(239,335)
(240,334)(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)(265,369)(266,368)(267,367)(268,372)(269,371)(270,370)(271,363)
(272,362)(273,361)(274,366)(275,365)(276,364)(277,381)(278,380)(279,379)
(280,384)(281,383)(282,382)(283,375)(284,374)(285,373)(286,378)(287,377)
(288,376);
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*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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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 >;
References : None.
to this polytope