Polytope of Type {24,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,3}*768
if this polytope has a name.
Group : SmallGroup(768,1085768)
Rank : 3
Schlafli Type : {24,3}
Number of vertices, edges, etc : 128, 192, 16
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 24
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 : {12,3}*384
   4-fold quotients : {6,3}*192
   8-fold quotients : {12,3}*96
   16-fold quotients : {6,3}*48
   32-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope