Polytope of Type {24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*768d
if this polytope has a name.
Group : SmallGroup(768,1087779)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 32, 192, 16
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, {24,6}*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 := (  3,  4)(  5,  7)(  6,  8)(  9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)
( 14, 24)( 15, 21)( 16, 22)( 25, 26)( 29, 32)( 30, 31)( 33, 42)( 34, 41)
( 35, 43)( 36, 44)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 49, 50)( 53, 56)
( 54, 55)( 57, 66)( 58, 65)( 59, 67)( 60, 68)( 61, 72)( 62, 71)( 63, 70)
( 64, 69)( 75, 76)( 77, 79)( 78, 80)( 81, 89)( 82, 90)( 83, 92)( 84, 91)
( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97,121)( 98,122)( 99,124)(100,123)
(101,127)(102,128)(103,125)(104,126)(105,137)(106,138)(107,140)(108,139)
(109,143)(110,144)(111,141)(112,142)(113,129)(114,130)(115,132)(116,131)
(117,135)(118,136)(119,133)(120,134)(145,170)(146,169)(147,171)(148,172)
(149,176)(150,175)(151,174)(152,173)(153,186)(154,185)(155,187)(156,188)
(157,192)(158,191)(159,190)(160,189)(161,178)(162,177)(163,179)(164,180)
(165,184)(166,183)(167,182)(168,181)(195,196)(197,199)(198,200)(201,209)
(202,210)(203,212)(204,211)(205,215)(206,216)(207,213)(208,214)(217,218)
(221,224)(222,223)(225,234)(226,233)(227,235)(228,236)(229,240)(230,239)
(231,238)(232,237)(241,242)(245,248)(246,247)(249,258)(250,257)(251,259)
(252,260)(253,264)(254,263)(255,262)(256,261)(267,268)(269,271)(270,272)
(273,281)(274,282)(275,284)(276,283)(277,287)(278,288)(279,285)(280,286)
(289,313)(290,314)(291,316)(292,315)(293,319)(294,320)(295,317)(296,318)
(297,329)(298,330)(299,332)(300,331)(301,335)(302,336)(303,333)(304,334)
(305,321)(306,322)(307,324)(308,323)(309,327)(310,328)(311,325)(312,326)
(337,362)(338,361)(339,363)(340,364)(341,368)(342,367)(343,366)(344,365)
(345,378)(346,377)(347,379)(348,380)(349,384)(350,383)(351,382)(352,381)
(353,370)(354,369)(355,371)(356,372)(357,376)(358,375)(359,374)(360,373);;
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 := (  1,220)(  2,219)(  3,218)(  4,217)(  5,221)(  6,222)(  7,224)(  8,223)
(  9,236)( 10,235)( 11,234)( 12,233)( 13,237)( 14,238)( 15,240)( 16,239)
( 17,228)( 18,227)( 19,226)( 20,225)( 21,229)( 22,230)( 23,232)( 24,231)
( 25,195)( 26,196)( 27,193)( 28,194)( 29,198)( 30,197)( 31,199)( 32,200)
( 33,211)( 34,212)( 35,209)( 36,210)( 37,214)( 38,213)( 39,215)( 40,216)
( 41,203)( 42,204)( 43,201)( 44,202)( 45,206)( 46,205)( 47,207)( 48,208)
( 49,268)( 50,267)( 51,266)( 52,265)( 53,269)( 54,270)( 55,272)( 56,271)
( 57,284)( 58,283)( 59,282)( 60,281)( 61,285)( 62,286)( 63,288)( 64,287)
( 65,276)( 66,275)( 67,274)( 68,273)( 69,277)( 70,278)( 71,280)( 72,279)
( 73,243)( 74,244)( 75,241)( 76,242)( 77,246)( 78,245)( 79,247)( 80,248)
( 81,259)( 82,260)( 83,257)( 84,258)( 85,262)( 86,261)( 87,263)( 88,264)
( 89,251)( 90,252)( 91,249)( 92,250)( 93,254)( 94,253)( 95,255)( 96,256)
( 97,340)( 98,339)( 99,338)(100,337)(101,341)(102,342)(103,344)(104,343)
(105,356)(106,355)(107,354)(108,353)(109,357)(110,358)(111,360)(112,359)
(113,348)(114,347)(115,346)(116,345)(117,349)(118,350)(119,352)(120,351)
(121,364)(122,363)(123,362)(124,361)(125,365)(126,366)(127,368)(128,367)
(129,380)(130,379)(131,378)(132,377)(133,381)(134,382)(135,384)(136,383)
(137,372)(138,371)(139,370)(140,369)(141,373)(142,374)(143,376)(144,375)
(145,291)(146,292)(147,289)(148,290)(149,294)(150,293)(151,295)(152,296)
(153,307)(154,308)(155,305)(156,306)(157,310)(158,309)(159,311)(160,312)
(161,299)(162,300)(163,297)(164,298)(165,302)(166,301)(167,303)(168,304)
(169,315)(170,316)(171,313)(172,314)(173,318)(174,317)(175,319)(176,320)
(177,331)(178,332)(179,329)(180,330)(181,334)(182,333)(183,335)(184,336)
(185,323)(186,324)(187,321)(188,322)(189,326)(190,325)(191,327)(192,328);;
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*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope