Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*768o
if this polytope has a name.
Group : SmallGroup(768,1086745)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 32, 192, 48
Order of s₀s₁s₂ : 24
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 : {8,6}*384g, {4,12}*384e
   4-fold quotients : {4,6}*192b
   8-fold quotients : {8,6}*96, {4,6}*96
   16-fold quotients : {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   24-fold quotients : {8,2}*32
   32-fold quotients : {4,3}*24, {2,6}*24
   48-fold quotients : {4,2}*16
   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, 17)(  2, 18)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 24)(  8, 23)
( 11, 14)( 12, 13)( 15, 16)( 25, 41)( 26, 42)( 27, 46)( 28, 45)( 29, 44)
( 30, 43)( 31, 48)( 32, 47)( 35, 38)( 36, 37)( 39, 40)( 49, 65)( 50, 66)
( 51, 70)( 52, 69)( 53, 68)( 54, 67)( 55, 72)( 56, 71)( 59, 62)( 60, 61)
( 63, 64)( 73, 89)( 74, 90)( 75, 94)( 76, 93)( 77, 92)( 78, 91)( 79, 96)
( 80, 95)( 83, 86)( 84, 85)( 87, 88)( 97,114)( 98,113)( 99,117)(100,118)
(101,115)(102,116)(103,119)(104,120)(105,106)(107,109)(108,110)(121,138)
(122,137)(123,141)(124,142)(125,139)(126,140)(127,143)(128,144)(129,130)
(131,133)(132,134)(145,162)(146,161)(147,165)(148,166)(149,163)(150,164)
(151,167)(152,168)(153,154)(155,157)(156,158)(169,186)(170,185)(171,189)
(172,190)(173,187)(174,188)(175,191)(176,192)(177,178)(179,181)(180,182)
(193,210)(194,209)(195,213)(196,214)(197,211)(198,212)(199,215)(200,216)
(201,202)(203,205)(204,206)(217,234)(218,233)(219,237)(220,238)(221,235)
(222,236)(223,239)(224,240)(225,226)(227,229)(228,230)(241,258)(242,257)
(243,261)(244,262)(245,259)(246,260)(247,263)(248,264)(249,250)(251,253)
(252,254)(265,282)(266,281)(267,285)(268,286)(269,283)(270,284)(271,287)
(272,288)(273,274)(275,277)(276,278)(289,305)(290,306)(291,310)(292,309)
(293,308)(294,307)(295,312)(296,311)(299,302)(300,301)(303,304)(313,329)
(314,330)(315,334)(316,333)(317,332)(318,331)(319,336)(320,335)(323,326)
(324,325)(327,328)(337,353)(338,354)(339,358)(340,357)(341,356)(342,355)
(343,360)(344,359)(347,350)(348,349)(351,352)(361,377)(362,378)(363,382)
(364,381)(365,380)(366,379)(367,384)(368,383)(371,374)(372,373)(375,376);;
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*s0*s1*s2*s0*s1*s2*s1*s2*s0*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, 17)(  2, 18)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 24)
(  8, 23)( 11, 14)( 12, 13)( 15, 16)( 25, 41)( 26, 42)( 27, 46)( 28, 45)
( 29, 44)( 30, 43)( 31, 48)( 32, 47)( 35, 38)( 36, 37)( 39, 40)( 49, 65)
( 50, 66)( 51, 70)( 52, 69)( 53, 68)( 54, 67)( 55, 72)( 56, 71)( 59, 62)
( 60, 61)( 63, 64)( 73, 89)( 74, 90)( 75, 94)( 76, 93)( 77, 92)( 78, 91)
( 79, 96)( 80, 95)( 83, 86)( 84, 85)( 87, 88)( 97,114)( 98,113)( 99,117)
(100,118)(101,115)(102,116)(103,119)(104,120)(105,106)(107,109)(108,110)
(121,138)(122,137)(123,141)(124,142)(125,139)(126,140)(127,143)(128,144)
(129,130)(131,133)(132,134)(145,162)(146,161)(147,165)(148,166)(149,163)
(150,164)(151,167)(152,168)(153,154)(155,157)(156,158)(169,186)(170,185)
(171,189)(172,190)(173,187)(174,188)(175,191)(176,192)(177,178)(179,181)
(180,182)(193,210)(194,209)(195,213)(196,214)(197,211)(198,212)(199,215)
(200,216)(201,202)(203,205)(204,206)(217,234)(218,233)(219,237)(220,238)
(221,235)(222,236)(223,239)(224,240)(225,226)(227,229)(228,230)(241,258)
(242,257)(243,261)(244,262)(245,259)(246,260)(247,263)(248,264)(249,250)
(251,253)(252,254)(265,282)(266,281)(267,285)(268,286)(269,283)(270,284)
(271,287)(272,288)(273,274)(275,277)(276,278)(289,305)(290,306)(291,310)
(292,309)(293,308)(294,307)(295,312)(296,311)(299,302)(300,301)(303,304)
(313,329)(314,330)(315,334)(316,333)(317,332)(318,331)(319,336)(320,335)
(323,326)(324,325)(327,328)(337,353)(338,354)(339,358)(340,357)(341,356)
(342,355)(343,360)(344,359)(347,350)(348,349)(351,352)(361,377)(362,378)
(363,382)(364,381)(365,380)(366,379)(367,384)(368,383)(371,374)(372,373)
(375,376);
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*s0*s1*s2*s0*s1*s2*s1*s2*s0*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