Polytope of Type {12,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*768d
if this polytope has a name.
Group : SmallGroup(768,1087779)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 16, 192, 32
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,12}*384a, {6,24}*384b
   4-fold quotients : {6,12}*192a, {12,6}*192a
   8-fold quotients : {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {4,4}*32
   32-fold quotients : {3,3}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope