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Polytope of Type {24,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*768n
if this polytope has a name.
Group : SmallGroup(768,1086745)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 48, 192, 16
Order of s0s1s2 : 12
Order of s0s1s2s1 : 8
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 : {12,8}*384h, {24,4}*384e
   4-fold quotients : {12,4}*192c, {6,8}*192b
   8-fold quotients : {3,8}*96, {6,4}*96
   16-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,4}*24, {6,2}*24
   64-fold quotients : {3,2}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,194)(  2,193)(  3,195)(  4,196)(  5,200)(  6,199)(  7,198)(  8,197)
(  9,210)( 10,209)( 11,211)( 12,212)( 13,216)( 14,215)( 15,214)( 16,213)
( 17,202)( 18,201)( 19,203)( 20,204)( 21,208)( 22,207)( 23,206)( 24,205)
( 25,218)( 26,217)( 27,219)( 28,220)( 29,224)( 30,223)( 31,222)( 32,221)
( 33,234)( 34,233)( 35,235)( 36,236)( 37,240)( 38,239)( 39,238)( 40,237)
( 41,226)( 42,225)( 43,227)( 44,228)( 45,232)( 46,231)( 47,230)( 48,229)
( 49,266)( 50,265)( 51,267)( 52,268)( 53,272)( 54,271)( 55,270)( 56,269)
( 57,282)( 58,281)( 59,283)( 60,284)( 61,288)( 62,287)( 63,286)( 64,285)
( 65,274)( 66,273)( 67,275)( 68,276)( 69,280)( 70,279)( 71,278)( 72,277)
( 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)
(145,289)(146,290)(147,292)(148,291)(149,295)(150,296)(151,293)(152,294)
(153,305)(154,306)(155,308)(156,307)(157,311)(158,312)(159,309)(160,310)
(161,297)(162,298)(163,300)(164,299)(165,303)(166,304)(167,301)(168,302)
(169,313)(170,314)(171,316)(172,315)(173,319)(174,320)(175,317)(176,318)
(177,329)(178,330)(179,332)(180,331)(181,335)(182,336)(183,333)(184,334)
(185,321)(186,322)(187,324)(188,323)(189,327)(190,328)(191,325)(192,326);;
s1 := (  1,113)(  2,114)(  3,118)(  4,117)(  5,116)(  6,115)(  7,120)(  8,119)
(  9,105)( 10,106)( 11,110)( 12,109)( 13,108)( 14,107)( 15,112)( 16,111)
( 17, 97)( 18, 98)( 19,102)( 20,101)( 21,100)( 22, 99)( 23,104)( 24,103)
( 25,137)( 26,138)( 27,142)( 28,141)( 29,140)( 30,139)( 31,144)( 32,143)
( 33,129)( 34,130)( 35,134)( 36,133)( 37,132)( 38,131)( 39,136)( 40,135)
( 41,121)( 42,122)( 43,126)( 44,125)( 45,124)( 46,123)( 47,128)( 48,127)
( 49,185)( 50,186)( 51,190)( 52,189)( 53,188)( 54,187)( 55,192)( 56,191)
( 57,177)( 58,178)( 59,182)( 60,181)( 61,180)( 62,179)( 63,184)( 64,183)
( 65,169)( 66,170)( 67,174)( 68,173)( 69,172)( 70,171)( 71,176)( 72,175)
( 73,161)( 74,162)( 75,166)( 76,165)( 77,164)( 78,163)( 79,168)( 80,167)
( 81,153)( 82,154)( 83,158)( 84,157)( 85,156)( 86,155)( 87,160)( 88,159)
( 89,145)( 90,146)( 91,150)( 92,149)( 93,148)( 94,147)( 95,152)( 96,151)
(193,306)(194,305)(195,309)(196,310)(197,307)(198,308)(199,311)(200,312)
(201,298)(202,297)(203,301)(204,302)(205,299)(206,300)(207,303)(208,304)
(209,290)(210,289)(211,293)(212,294)(213,291)(214,292)(215,295)(216,296)
(217,330)(218,329)(219,333)(220,334)(221,331)(222,332)(223,335)(224,336)
(225,322)(226,321)(227,325)(228,326)(229,323)(230,324)(231,327)(232,328)
(233,314)(234,313)(235,317)(236,318)(237,315)(238,316)(239,319)(240,320)
(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 := (  1,196)(  2,195)(  3,193)(  4,194)(  5,200)(  6,199)(  7,197)(  8,198)
(  9,204)( 10,203)( 11,201)( 12,202)( 13,208)( 14,207)( 15,205)( 16,206)
( 17,212)( 18,211)( 19,209)( 20,210)( 21,216)( 22,215)( 23,213)( 24,214)
( 25,220)( 26,219)( 27,217)( 28,218)( 29,224)( 30,223)( 31,221)( 32,222)
( 33,228)( 34,227)( 35,225)( 36,226)( 37,232)( 38,231)( 39,229)( 40,230)
( 41,236)( 42,235)( 43,233)( 44,234)( 45,240)( 46,239)( 47,237)( 48,238)
( 49,268)( 50,267)( 51,265)( 52,266)( 53,272)( 54,271)( 55,269)( 56,270)
( 57,276)( 58,275)( 59,273)( 60,274)( 61,280)( 62,279)( 63,277)( 64,278)
( 65,284)( 66,283)( 67,281)( 68,282)( 69,288)( 70,287)( 71,285)( 72,286)
( 73,244)( 74,243)( 75,241)( 76,242)( 77,248)( 78,247)( 79,245)( 80,246)
( 81,252)( 82,251)( 83,249)( 84,250)( 85,256)( 86,255)( 87,253)( 88,254)
( 89,260)( 90,259)( 91,257)( 92,258)( 93,264)( 94,263)( 95,261)( 96,262)
( 97,340)( 98,339)( 99,337)(100,338)(101,344)(102,343)(103,341)(104,342)
(105,348)(106,347)(107,345)(108,346)(109,352)(110,351)(111,349)(112,350)
(113,356)(114,355)(115,353)(116,354)(117,360)(118,359)(119,357)(120,358)
(121,364)(122,363)(123,361)(124,362)(125,368)(126,367)(127,365)(128,366)
(129,372)(130,371)(131,369)(132,370)(133,376)(134,375)(135,373)(136,374)
(137,380)(138,379)(139,377)(140,378)(141,384)(142,383)(143,381)(144,382)
(145,292)(146,291)(147,289)(148,290)(149,296)(150,295)(151,293)(152,294)
(153,300)(154,299)(155,297)(156,298)(157,304)(158,303)(159,301)(160,302)
(161,308)(162,307)(163,305)(164,306)(165,312)(166,311)(167,309)(168,310)
(169,316)(170,315)(171,313)(172,314)(173,320)(174,319)(175,317)(176,318)
(177,324)(178,323)(179,321)(180,322)(181,328)(182,327)(183,325)(184,326)
(185,332)(186,331)(187,329)(188,330)(189,336)(190,335)(191,333)(192,334);;
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*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(384)!(  1,194)(  2,193)(  3,195)(  4,196)(  5,200)(  6,199)(  7,198)
(  8,197)(  9,210)( 10,209)( 11,211)( 12,212)( 13,216)( 14,215)( 15,214)
( 16,213)( 17,202)( 18,201)( 19,203)( 20,204)( 21,208)( 22,207)( 23,206)
( 24,205)( 25,218)( 26,217)( 27,219)( 28,220)( 29,224)( 30,223)( 31,222)
( 32,221)( 33,234)( 34,233)( 35,235)( 36,236)( 37,240)( 38,239)( 39,238)
( 40,237)( 41,226)( 42,225)( 43,227)( 44,228)( 45,232)( 46,231)( 47,230)
( 48,229)( 49,266)( 50,265)( 51,267)( 52,268)( 53,272)( 54,271)( 55,270)
( 56,269)( 57,282)( 58,281)( 59,283)( 60,284)( 61,288)( 62,287)( 63,286)
( 64,285)( 65,274)( 66,273)( 67,275)( 68,276)( 69,280)( 70,279)( 71,278)
( 72,277)( 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)(145,289)(146,290)(147,292)(148,291)(149,295)(150,296)(151,293)
(152,294)(153,305)(154,306)(155,308)(156,307)(157,311)(158,312)(159,309)
(160,310)(161,297)(162,298)(163,300)(164,299)(165,303)(166,304)(167,301)
(168,302)(169,313)(170,314)(171,316)(172,315)(173,319)(174,320)(175,317)
(176,318)(177,329)(178,330)(179,332)(180,331)(181,335)(182,336)(183,333)
(184,334)(185,321)(186,322)(187,324)(188,323)(189,327)(190,328)(191,325)
(192,326);
s1 := Sym(384)!(  1,113)(  2,114)(  3,118)(  4,117)(  5,116)(  6,115)(  7,120)
(  8,119)(  9,105)( 10,106)( 11,110)( 12,109)( 13,108)( 14,107)( 15,112)
( 16,111)( 17, 97)( 18, 98)( 19,102)( 20,101)( 21,100)( 22, 99)( 23,104)
( 24,103)( 25,137)( 26,138)( 27,142)( 28,141)( 29,140)( 30,139)( 31,144)
( 32,143)( 33,129)( 34,130)( 35,134)( 36,133)( 37,132)( 38,131)( 39,136)
( 40,135)( 41,121)( 42,122)( 43,126)( 44,125)( 45,124)( 46,123)( 47,128)
( 48,127)( 49,185)( 50,186)( 51,190)( 52,189)( 53,188)( 54,187)( 55,192)
( 56,191)( 57,177)( 58,178)( 59,182)( 60,181)( 61,180)( 62,179)( 63,184)
( 64,183)( 65,169)( 66,170)( 67,174)( 68,173)( 69,172)( 70,171)( 71,176)
( 72,175)( 73,161)( 74,162)( 75,166)( 76,165)( 77,164)( 78,163)( 79,168)
( 80,167)( 81,153)( 82,154)( 83,158)( 84,157)( 85,156)( 86,155)( 87,160)
( 88,159)( 89,145)( 90,146)( 91,150)( 92,149)( 93,148)( 94,147)( 95,152)
( 96,151)(193,306)(194,305)(195,309)(196,310)(197,307)(198,308)(199,311)
(200,312)(201,298)(202,297)(203,301)(204,302)(205,299)(206,300)(207,303)
(208,304)(209,290)(210,289)(211,293)(212,294)(213,291)(214,292)(215,295)
(216,296)(217,330)(218,329)(219,333)(220,334)(221,331)(222,332)(223,335)
(224,336)(225,322)(226,321)(227,325)(228,326)(229,323)(230,324)(231,327)
(232,328)(233,314)(234,313)(235,317)(236,318)(237,315)(238,316)(239,319)
(240,320)(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)!(  1,196)(  2,195)(  3,193)(  4,194)(  5,200)(  6,199)(  7,197)
(  8,198)(  9,204)( 10,203)( 11,201)( 12,202)( 13,208)( 14,207)( 15,205)
( 16,206)( 17,212)( 18,211)( 19,209)( 20,210)( 21,216)( 22,215)( 23,213)
( 24,214)( 25,220)( 26,219)( 27,217)( 28,218)( 29,224)( 30,223)( 31,221)
( 32,222)( 33,228)( 34,227)( 35,225)( 36,226)( 37,232)( 38,231)( 39,229)
( 40,230)( 41,236)( 42,235)( 43,233)( 44,234)( 45,240)( 46,239)( 47,237)
( 48,238)( 49,268)( 50,267)( 51,265)( 52,266)( 53,272)( 54,271)( 55,269)
( 56,270)( 57,276)( 58,275)( 59,273)( 60,274)( 61,280)( 62,279)( 63,277)
( 64,278)( 65,284)( 66,283)( 67,281)( 68,282)( 69,288)( 70,287)( 71,285)
( 72,286)( 73,244)( 74,243)( 75,241)( 76,242)( 77,248)( 78,247)( 79,245)
( 80,246)( 81,252)( 82,251)( 83,249)( 84,250)( 85,256)( 86,255)( 87,253)
( 88,254)( 89,260)( 90,259)( 91,257)( 92,258)( 93,264)( 94,263)( 95,261)
( 96,262)( 97,340)( 98,339)( 99,337)(100,338)(101,344)(102,343)(103,341)
(104,342)(105,348)(106,347)(107,345)(108,346)(109,352)(110,351)(111,349)
(112,350)(113,356)(114,355)(115,353)(116,354)(117,360)(118,359)(119,357)
(120,358)(121,364)(122,363)(123,361)(124,362)(125,368)(126,367)(127,365)
(128,366)(129,372)(130,371)(131,369)(132,370)(133,376)(134,375)(135,373)
(136,374)(137,380)(138,379)(139,377)(140,378)(141,384)(142,383)(143,381)
(144,382)(145,292)(146,291)(147,289)(148,290)(149,296)(150,295)(151,293)
(152,294)(153,300)(154,299)(155,297)(156,298)(157,304)(158,303)(159,301)
(160,302)(161,308)(162,307)(163,305)(164,306)(165,312)(166,311)(167,309)
(168,310)(169,316)(170,315)(171,313)(172,314)(173,320)(174,319)(175,317)
(176,318)(177,324)(178,323)(179,321)(180,322)(181,328)(182,327)(183,325)
(184,326)(185,332)(186,331)(187,329)(188,330)(189,336)(190,335)(191,333)
(192,334);
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*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1 >; 
 
References : None.
to this polytope