Polytope of Type {8,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*768n
if this polytope has a name.
Group : SmallGroup(768,1086745)
Rank : 3
Schlafli Type : {8,24}
Number of vertices, edges, etc : 16, 192, 48
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 : {8,12}*384h, {4,24}*384e
   4-fold quotients : {4,12}*192c, {8,6}*192b
   8-fold quotients : {8,3}*96, {4,6}*96
   16-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {4,3}*24, {2,6}*24
   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 := (  1,199)(  2,200)(  3,197)(  4,198)(  5,196)(  6,195)(  7,194)(  8,193)
(  9,207)( 10,208)( 11,205)( 12,206)( 13,204)( 14,203)( 15,202)( 16,201)
( 17,215)( 18,216)( 19,213)( 20,214)( 21,212)( 22,211)( 23,210)( 24,209)
( 25,223)( 26,224)( 27,221)( 28,222)( 29,220)( 30,219)( 31,218)( 32,217)
( 33,231)( 34,232)( 35,229)( 36,230)( 37,228)( 38,227)( 39,226)( 40,225)
( 41,239)( 42,240)( 43,237)( 44,238)( 45,236)( 46,235)( 47,234)( 48,233)
( 49,271)( 50,272)( 51,269)( 52,270)( 53,268)( 54,267)( 55,266)( 56,265)
( 57,279)( 58,280)( 59,277)( 60,278)( 61,276)( 62,275)( 63,274)( 64,273)
( 65,287)( 66,288)( 67,285)( 68,286)( 69,284)( 70,283)( 71,282)( 72,281)
( 73,247)( 74,248)( 75,245)( 76,246)( 77,244)( 78,243)( 79,242)( 80,241)
( 81,255)( 82,256)( 83,253)( 84,254)( 85,252)( 86,251)( 87,250)( 88,249)
( 89,263)( 90,264)( 91,261)( 92,262)( 93,260)( 94,259)( 95,258)( 96,257)
( 97,343)( 98,344)( 99,341)(100,342)(101,340)(102,339)(103,338)(104,337)
(105,351)(106,352)(107,349)(108,350)(109,348)(110,347)(111,346)(112,345)
(113,359)(114,360)(115,357)(116,358)(117,356)(118,355)(119,354)(120,353)
(121,367)(122,368)(123,365)(124,366)(125,364)(126,363)(127,362)(128,361)
(129,375)(130,376)(131,373)(132,374)(133,372)(134,371)(135,370)(136,369)
(137,383)(138,384)(139,381)(140,382)(141,380)(142,379)(143,378)(144,377)
(145,295)(146,296)(147,293)(148,294)(149,292)(150,291)(151,290)(152,289)
(153,303)(154,304)(155,301)(156,302)(157,300)(158,299)(159,298)(160,297)
(161,311)(162,312)(163,309)(164,310)(165,308)(166,307)(167,306)(168,305)
(169,319)(170,320)(171,317)(172,318)(173,316)(174,315)(175,314)(176,313)
(177,327)(178,328)(179,325)(180,326)(181,324)(182,323)(183,322)(184,321)
(185,335)(186,336)(187,333)(188,334)(189,332)(190,331)(191,330)(192,329);;
s1 := (  1, 98)(  2, 97)(  3, 99)(  4,100)(  5,104)(  6,103)(  7,102)(  8,101)
(  9,114)( 10,113)( 11,115)( 12,116)( 13,120)( 14,119)( 15,118)( 16,117)
( 17,106)( 18,105)( 19,107)( 20,108)( 21,112)( 22,111)( 23,110)( 24,109)
( 25,122)( 26,121)( 27,123)( 28,124)( 29,128)( 30,127)( 31,126)( 32,125)
( 33,138)( 34,137)( 35,139)( 36,140)( 37,144)( 38,143)( 39,142)( 40,141)
( 41,130)( 42,129)( 43,131)( 44,132)( 45,136)( 46,135)( 47,134)( 48,133)
( 49,170)( 50,169)( 51,171)( 52,172)( 53,176)( 54,175)( 55,174)( 56,173)
( 57,186)( 58,185)( 59,187)( 60,188)( 61,192)( 62,191)( 63,190)( 64,189)
( 65,178)( 66,177)( 67,179)( 68,180)( 69,184)( 70,183)( 71,182)( 72,181)
( 73,146)( 74,145)( 75,147)( 76,148)( 77,152)( 78,151)( 79,150)( 80,149)
( 81,162)( 82,161)( 83,163)( 84,164)( 85,168)( 86,167)( 87,166)( 88,165)
( 89,154)( 90,153)( 91,155)( 92,156)( 93,160)( 94,159)( 95,158)( 96,157)
(193,289)(194,290)(195,292)(196,291)(197,295)(198,296)(199,293)(200,294)
(201,305)(202,306)(203,308)(204,307)(205,311)(206,312)(207,309)(208,310)
(209,297)(210,298)(211,300)(212,299)(213,303)(214,304)(215,301)(216,302)
(217,313)(218,314)(219,316)(220,315)(221,319)(222,320)(223,317)(224,318)
(225,329)(226,330)(227,332)(228,331)(229,335)(230,336)(231,333)(232,334)
(233,321)(234,322)(235,324)(236,323)(237,327)(238,328)(239,325)(240,326)
(241,361)(242,362)(243,364)(244,363)(245,367)(246,368)(247,365)(248,366)
(249,377)(250,378)(251,380)(252,379)(253,383)(254,384)(255,381)(256,382)
(257,369)(258,370)(259,372)(260,371)(261,375)(262,376)(263,373)(264,374)
(265,337)(266,338)(267,340)(268,339)(269,343)(270,344)(271,341)(272,342)
(273,353)(274,354)(275,356)(276,355)(277,359)(278,360)(279,357)(280,358)
(281,345)(282,346)(283,348)(284,347)(285,351)(286,352)(287,349)(288,350);;
s2 := (  1,209)(  2,210)(  3,214)(  4,213)(  5,212)(  6,211)(  7,216)(  8,215)
(  9,201)( 10,202)( 11,206)( 12,205)( 13,204)( 14,203)( 15,208)( 16,207)
( 17,193)( 18,194)( 19,198)( 20,197)( 21,196)( 22,195)( 23,200)( 24,199)
( 25,233)( 26,234)( 27,238)( 28,237)( 29,236)( 30,235)( 31,240)( 32,239)
( 33,225)( 34,226)( 35,230)( 36,229)( 37,228)( 38,227)( 39,232)( 40,231)
( 41,217)( 42,218)( 43,222)( 44,221)( 45,220)( 46,219)( 47,224)( 48,223)
( 49,281)( 50,282)( 51,286)( 52,285)( 53,284)( 54,283)( 55,288)( 56,287)
( 57,273)( 58,274)( 59,278)( 60,277)( 61,276)( 62,275)( 63,280)( 64,279)
( 65,265)( 66,266)( 67,270)( 68,269)( 69,268)( 70,267)( 71,272)( 72,271)
( 73,257)( 74,258)( 75,262)( 76,261)( 77,260)( 78,259)( 79,264)( 80,263)
( 81,249)( 82,250)( 83,254)( 84,253)( 85,252)( 86,251)( 87,256)( 88,255)
( 89,241)( 90,242)( 91,246)( 92,245)( 93,244)( 94,243)( 95,248)( 96,247)
( 97,354)( 98,353)( 99,357)(100,358)(101,355)(102,356)(103,359)(104,360)
(105,346)(106,345)(107,349)(108,350)(109,347)(110,348)(111,351)(112,352)
(113,338)(114,337)(115,341)(116,342)(117,339)(118,340)(119,343)(120,344)
(121,378)(122,377)(123,381)(124,382)(125,379)(126,380)(127,383)(128,384)
(129,370)(130,369)(131,373)(132,374)(133,371)(134,372)(135,375)(136,376)
(137,362)(138,361)(139,365)(140,366)(141,363)(142,364)(143,367)(144,368)
(145,306)(146,305)(147,309)(148,310)(149,307)(150,308)(151,311)(152,312)
(153,298)(154,297)(155,301)(156,302)(157,299)(158,300)(159,303)(160,304)
(161,290)(162,289)(163,293)(164,294)(165,291)(166,292)(167,295)(168,296)
(169,330)(170,329)(171,333)(172,334)(173,331)(174,332)(175,335)(176,336)
(177,322)(178,321)(179,325)(180,326)(181,323)(182,324)(183,327)(184,328)
(185,314)(186,313)(187,317)(188,318)(189,315)(190,316)(191,319)(192,320);;
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*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope