Polytope of Type {24,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*768o
if this polytope has a name.
Group : SmallGroup(768,1086857)
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}*384g, {24,4}*384e
   4-fold quotients : {12,4}*192c, {6,8}*192c
   8-fold quotients : {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)
( 97,362)( 98,361)( 99,363)(100,364)(101,368)(102,367)(103,366)(104,365)
(105,378)(106,377)(107,379)(108,380)(109,384)(110,383)(111,382)(112,381)
(113,370)(114,369)(115,371)(116,372)(117,376)(118,375)(119,374)(120,373)
(121,338)(122,337)(123,339)(124,340)(125,344)(126,343)(127,342)(128,341)
(129,354)(130,353)(131,355)(132,356)(133,360)(134,359)(135,358)(136,357)
(137,346)(138,345)(139,347)(140,348)(141,352)(142,351)(143,350)(144,349)
(145,314)(146,313)(147,315)(148,316)(149,320)(150,319)(151,318)(152,317)
(153,330)(154,329)(155,331)(156,332)(157,336)(158,335)(159,334)(160,333)
(161,322)(162,321)(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)
(169,290)(170,289)(171,291)(172,292)(173,296)(174,295)(175,294)(176,293)
(177,306)(178,305)(179,307)(180,308)(181,312)(182,311)(183,310)(184,309)
(185,298)(186,297)(187,299)(188,300)(189,304)(190,303)(191,302)(192,301);;
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)
( 49,161)( 50,162)( 51,166)( 52,165)( 53,164)( 54,163)( 55,168)( 56,167)
( 57,153)( 58,154)( 59,158)( 60,157)( 61,156)( 62,155)( 63,160)( 64,159)
( 65,145)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,152)( 72,151)
( 73,185)( 74,186)( 75,190)( 76,189)( 77,188)( 78,187)( 79,192)( 80,191)
( 81,177)( 82,178)( 83,182)( 84,181)( 85,180)( 86,179)( 87,184)( 88,183)
( 89,169)( 90,170)( 91,174)( 92,173)( 93,172)( 94,171)( 95,176)( 96,175)
(193,330)(194,329)(195,333)(196,334)(197,331)(198,332)(199,335)(200,336)
(201,322)(202,321)(203,325)(204,326)(205,323)(206,324)(207,327)(208,328)
(209,314)(210,313)(211,317)(212,318)(213,315)(214,316)(215,319)(216,320)
(217,306)(218,305)(219,309)(220,310)(221,307)(222,308)(223,311)(224,312)
(225,298)(226,297)(227,301)(228,302)(229,299)(230,300)(231,303)(232,304)
(233,290)(234,289)(235,293)(236,294)(237,291)(238,292)(239,295)(240,296)
(241,354)(242,353)(243,357)(244,358)(245,355)(246,356)(247,359)(248,360)
(249,346)(250,345)(251,349)(252,350)(253,347)(254,348)(255,351)(256,352)
(257,338)(258,337)(259,341)(260,342)(261,339)(262,340)(263,343)(264,344)
(265,378)(266,377)(267,381)(268,382)(269,379)(270,380)(271,383)(272,384)
(273,370)(274,369)(275,373)(276,374)(277,371)(278,372)(279,375)(280,376)
(281,362)(282,361)(283,365)(284,366)(285,363)(286,364)(287,367)(288,368);;
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, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*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)( 97,362)( 98,361)( 99,363)(100,364)(101,368)(102,367)(103,366)
(104,365)(105,378)(106,377)(107,379)(108,380)(109,384)(110,383)(111,382)
(112,381)(113,370)(114,369)(115,371)(116,372)(117,376)(118,375)(119,374)
(120,373)(121,338)(122,337)(123,339)(124,340)(125,344)(126,343)(127,342)
(128,341)(129,354)(130,353)(131,355)(132,356)(133,360)(134,359)(135,358)
(136,357)(137,346)(138,345)(139,347)(140,348)(141,352)(142,351)(143,350)
(144,349)(145,314)(146,313)(147,315)(148,316)(149,320)(150,319)(151,318)
(152,317)(153,330)(154,329)(155,331)(156,332)(157,336)(158,335)(159,334)
(160,333)(161,322)(162,321)(163,323)(164,324)(165,328)(166,327)(167,326)
(168,325)(169,290)(170,289)(171,291)(172,292)(173,296)(174,295)(175,294)
(176,293)(177,306)(178,305)(179,307)(180,308)(181,312)(182,311)(183,310)
(184,309)(185,298)(186,297)(187,299)(188,300)(189,304)(190,303)(191,302)
(192,301);
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)( 49,161)( 50,162)( 51,166)( 52,165)( 53,164)( 54,163)( 55,168)
( 56,167)( 57,153)( 58,154)( 59,158)( 60,157)( 61,156)( 62,155)( 63,160)
( 64,159)( 65,145)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,152)
( 72,151)( 73,185)( 74,186)( 75,190)( 76,189)( 77,188)( 78,187)( 79,192)
( 80,191)( 81,177)( 82,178)( 83,182)( 84,181)( 85,180)( 86,179)( 87,184)
( 88,183)( 89,169)( 90,170)( 91,174)( 92,173)( 93,172)( 94,171)( 95,176)
( 96,175)(193,330)(194,329)(195,333)(196,334)(197,331)(198,332)(199,335)
(200,336)(201,322)(202,321)(203,325)(204,326)(205,323)(206,324)(207,327)
(208,328)(209,314)(210,313)(211,317)(212,318)(213,315)(214,316)(215,319)
(216,320)(217,306)(218,305)(219,309)(220,310)(221,307)(222,308)(223,311)
(224,312)(225,298)(226,297)(227,301)(228,302)(229,299)(230,300)(231,303)
(232,304)(233,290)(234,289)(235,293)(236,294)(237,291)(238,292)(239,295)
(240,296)(241,354)(242,353)(243,357)(244,358)(245,355)(246,356)(247,359)
(248,360)(249,346)(250,345)(251,349)(252,350)(253,347)(254,348)(255,351)
(256,352)(257,338)(258,337)(259,341)(260,342)(261,339)(262,340)(263,343)
(264,344)(265,378)(266,377)(267,381)(268,382)(269,379)(270,380)(271,383)
(272,384)(273,370)(274,369)(275,373)(276,374)(277,371)(278,372)(279,375)
(280,376)(281,362)(282,361)(283,365)(284,366)(285,363)(286,364)(287,367)
(288,368);
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, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope