Polytope of Type {8,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*768o
if this polytope has a name.
Group : SmallGroup(768,1086857)
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
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,12}*384g, {4,24}*384e
   4-fold quotients : {4,12}*192c, {8,6}*192c
   8-fold quotients : {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 := (  1,121)(  2,122)(  3,124)(  4,123)(  5,127)(  6,128)(  7,125)(  8,126)
(  9,137)( 10,138)( 11,140)( 12,139)( 13,143)( 14,144)( 15,141)( 16,142)
( 17,129)( 18,130)( 19,132)( 20,131)( 21,135)( 22,136)( 23,133)( 24,134)
( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,103)( 30,104)( 31,101)( 32,102)
( 33,113)( 34,114)( 35,116)( 36,115)( 37,119)( 38,120)( 39,117)( 40,118)
( 41,105)( 42,106)( 43,108)( 44,107)( 45,111)( 46,112)( 47,109)( 48,110)
( 49,145)( 50,146)( 51,148)( 52,147)( 53,151)( 54,152)( 55,149)( 56,150)
( 57,161)( 58,162)( 59,164)( 60,163)( 61,167)( 62,168)( 63,165)( 64,166)
( 65,153)( 66,154)( 67,156)( 68,155)( 69,159)( 70,160)( 71,157)( 72,158)
( 73,169)( 74,170)( 75,172)( 76,171)( 77,175)( 78,176)( 79,173)( 80,174)
( 81,185)( 82,186)( 83,188)( 84,187)( 85,191)( 86,192)( 87,189)( 88,190)
( 89,177)( 90,178)( 91,180)( 92,179)( 93,183)( 94,184)( 95,181)( 96,182)
(193,314)(194,313)(195,315)(196,316)(197,320)(198,319)(199,318)(200,317)
(201,330)(202,329)(203,331)(204,332)(205,336)(206,335)(207,334)(208,333)
(209,322)(210,321)(211,323)(212,324)(213,328)(214,327)(215,326)(216,325)
(217,290)(218,289)(219,291)(220,292)(221,296)(222,295)(223,294)(224,293)
(225,306)(226,305)(227,307)(228,308)(229,312)(230,311)(231,310)(232,309)
(233,298)(234,297)(235,299)(236,300)(237,304)(238,303)(239,302)(240,301)
(241,338)(242,337)(243,339)(244,340)(245,344)(246,343)(247,342)(248,341)
(249,354)(250,353)(251,355)(252,356)(253,360)(254,359)(255,358)(256,357)
(257,346)(258,345)(259,347)(260,348)(261,352)(262,351)(263,350)(264,349)
(265,362)(266,361)(267,363)(268,364)(269,368)(270,367)(271,366)(272,365)
(273,378)(274,377)(275,379)(276,380)(277,384)(278,383)(279,382)(280,381)
(281,370)(282,369)(283,371)(284,372)(285,376)(286,375)(287,374)(288,373);;
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)
( 97,377)( 98,378)( 99,382)(100,381)(101,380)(102,379)(103,384)(104,383)
(105,369)(106,370)(107,374)(108,373)(109,372)(110,371)(111,376)(112,375)
(113,361)(114,362)(115,366)(116,365)(117,364)(118,363)(119,368)(120,367)
(121,353)(122,354)(123,358)(124,357)(125,356)(126,355)(127,360)(128,359)
(129,345)(130,346)(131,350)(132,349)(133,348)(134,347)(135,352)(136,351)
(137,337)(138,338)(139,342)(140,341)(141,340)(142,339)(143,344)(144,343)
(145,329)(146,330)(147,334)(148,333)(149,332)(150,331)(151,336)(152,335)
(153,321)(154,322)(155,326)(156,325)(157,324)(158,323)(159,328)(160,327)
(161,313)(162,314)(163,318)(164,317)(165,316)(166,315)(167,320)(168,319)
(169,305)(170,306)(171,310)(172,309)(173,308)(174,307)(175,312)(176,311)
(177,297)(178,298)(179,302)(180,301)(181,300)(182,299)(183,304)(184,303)
(185,289)(186,290)(187,294)(188,293)(189,292)(190,291)(191,296)(192,295);;
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, 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, 
s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2 ];;
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)!(  1,121)(  2,122)(  3,124)(  4,123)(  5,127)(  6,128)(  7,125)
(  8,126)(  9,137)( 10,138)( 11,140)( 12,139)( 13,143)( 14,144)( 15,141)
( 16,142)( 17,129)( 18,130)( 19,132)( 20,131)( 21,135)( 22,136)( 23,133)
( 24,134)( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,103)( 30,104)( 31,101)
( 32,102)( 33,113)( 34,114)( 35,116)( 36,115)( 37,119)( 38,120)( 39,117)
( 40,118)( 41,105)( 42,106)( 43,108)( 44,107)( 45,111)( 46,112)( 47,109)
( 48,110)( 49,145)( 50,146)( 51,148)( 52,147)( 53,151)( 54,152)( 55,149)
( 56,150)( 57,161)( 58,162)( 59,164)( 60,163)( 61,167)( 62,168)( 63,165)
( 64,166)( 65,153)( 66,154)( 67,156)( 68,155)( 69,159)( 70,160)( 71,157)
( 72,158)( 73,169)( 74,170)( 75,172)( 76,171)( 77,175)( 78,176)( 79,173)
( 80,174)( 81,185)( 82,186)( 83,188)( 84,187)( 85,191)( 86,192)( 87,189)
( 88,190)( 89,177)( 90,178)( 91,180)( 92,179)( 93,183)( 94,184)( 95,181)
( 96,182)(193,314)(194,313)(195,315)(196,316)(197,320)(198,319)(199,318)
(200,317)(201,330)(202,329)(203,331)(204,332)(205,336)(206,335)(207,334)
(208,333)(209,322)(210,321)(211,323)(212,324)(213,328)(214,327)(215,326)
(216,325)(217,290)(218,289)(219,291)(220,292)(221,296)(222,295)(223,294)
(224,293)(225,306)(226,305)(227,307)(228,308)(229,312)(230,311)(231,310)
(232,309)(233,298)(234,297)(235,299)(236,300)(237,304)(238,303)(239,302)
(240,301)(241,338)(242,337)(243,339)(244,340)(245,344)(246,343)(247,342)
(248,341)(249,354)(250,353)(251,355)(252,356)(253,360)(254,359)(255,358)
(256,357)(257,346)(258,345)(259,347)(260,348)(261,352)(262,351)(263,350)
(264,349)(265,362)(266,361)(267,363)(268,364)(269,368)(270,367)(271,366)
(272,365)(273,378)(274,377)(275,379)(276,380)(277,384)(278,383)(279,382)
(280,381)(281,370)(282,369)(283,371)(284,372)(285,376)(286,375)(287,374)
(288,373);
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)( 97,377)( 98,378)( 99,382)(100,381)(101,380)(102,379)(103,384)
(104,383)(105,369)(106,370)(107,374)(108,373)(109,372)(110,371)(111,376)
(112,375)(113,361)(114,362)(115,366)(116,365)(117,364)(118,363)(119,368)
(120,367)(121,353)(122,354)(123,358)(124,357)(125,356)(126,355)(127,360)
(128,359)(129,345)(130,346)(131,350)(132,349)(133,348)(134,347)(135,352)
(136,351)(137,337)(138,338)(139,342)(140,341)(141,340)(142,339)(143,344)
(144,343)(145,329)(146,330)(147,334)(148,333)(149,332)(150,331)(151,336)
(152,335)(153,321)(154,322)(155,326)(156,325)(157,324)(158,323)(159,328)
(160,327)(161,313)(162,314)(163,318)(164,317)(165,316)(166,315)(167,320)
(168,319)(169,305)(170,306)(171,310)(172,309)(173,308)(174,307)(175,312)
(176,311)(177,297)(178,298)(179,302)(180,301)(181,300)(182,299)(183,304)
(184,303)(185,289)(186,290)(187,294)(188,293)(189,292)(190,291)(191,296)
(192,295);
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, 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, 
s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2 >;

References : None.
to this polytope