Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*768p
if this polytope has a name.
Group : SmallGroup(768,1086857)
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
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,6}*384f, {4,12}*384e
   4-fold quotients : {4,6}*192b, {8,6}*192b, {8,6}*192c
   8-fold quotients : {8,3}*96, {4,6}*96
   16-fold quotients : {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   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 := (  1,121)(  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, 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)( 97,137)( 98,138)( 99,142)(100,141)
(101,140)(102,139)(103,144)(104,143)(105,129)(106,130)(107,134)(108,133)
(109,132)(110,131)(111,136)(112,135)(113,121)(114,122)(115,126)(116,125)
(117,124)(118,123)(119,128)(120,127)(145,185)(146,186)(147,190)(148,189)
(149,188)(150,187)(151,192)(152,191)(153,177)(154,178)(155,182)(156,181)
(157,180)(158,179)(159,184)(160,183)(161,169)(162,170)(163,174)(164,173)
(165,172)(166,171)(167,176)(168,175)(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)
(289,330)(290,329)(291,333)(292,334)(293,331)(294,332)(295,335)(296,336)
(297,322)(298,321)(299,325)(300,326)(301,323)(302,324)(303,327)(304,328)
(305,314)(306,313)(307,317)(308,318)(309,315)(310,316)(311,319)(312,320)
(337,378)(338,377)(339,381)(340,382)(341,379)(342,380)(343,383)(344,384)
(345,370)(346,369)(347,373)(348,374)(349,371)(350,372)(351,375)(352,376)
(353,362)(354,361)(355,365)(356,366)(357,363)(358,364)(359,367)(360,368);;
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, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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)!(  1,121)(  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, 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)( 97,137)( 98,138)( 99,142)
(100,141)(101,140)(102,139)(103,144)(104,143)(105,129)(106,130)(107,134)
(108,133)(109,132)(110,131)(111,136)(112,135)(113,121)(114,122)(115,126)
(116,125)(117,124)(118,123)(119,128)(120,127)(145,185)(146,186)(147,190)
(148,189)(149,188)(150,187)(151,192)(152,191)(153,177)(154,178)(155,182)
(156,181)(157,180)(158,179)(159,184)(160,183)(161,169)(162,170)(163,174)
(164,173)(165,172)(166,171)(167,176)(168,175)(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)(289,330)(290,329)(291,333)(292,334)(293,331)(294,332)(295,335)
(296,336)(297,322)(298,321)(299,325)(300,326)(301,323)(302,324)(303,327)
(304,328)(305,314)(306,313)(307,317)(308,318)(309,315)(310,316)(311,319)
(312,320)(337,378)(338,377)(339,381)(340,382)(341,379)(342,380)(343,383)
(344,384)(345,370)(346,369)(347,373)(348,374)(349,371)(350,372)(351,375)
(352,376)(353,362)(354,361)(355,365)(356,366)(357,363)(358,364)(359,367)
(360,368);
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, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1 >;

References : None.
to this polytope