Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*768s
if this polytope has a name.
Group : SmallGroup(768,1087715)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 32, 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 : {4,12}*384d, {8,12}*384e, {8,12}*384f, {8,6}*384f, {8,12}*384g, {8,12}*384h
   4-fold quotients : {4,12}*192b, {4,6}*192b, {4,12}*192c, {8,6}*192b, {8,6}*192c
   8-fold quotients : {4,12}*96a, {4,12}*96b, {4,12}*96c, {8,3}*96, {4,6}*96
   16-fold quotients : {2,12}*48, {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   24-fold quotients : {4,4}*32
   32-fold quotients : {4,3}*24, {2,6}*24
   48-fold quotients : {2,4}*16, {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)
( 49,247)( 50,248)( 51,245)( 52,246)( 53,244)( 54,243)( 55,242)( 56,241)
( 57,255)( 58,256)( 59,253)( 60,254)( 61,252)( 62,251)( 63,250)( 64,249)
( 65,263)( 66,264)( 67,261)( 68,262)( 69,260)( 70,259)( 71,258)( 72,257)
( 73,271)( 74,272)( 75,269)( 76,270)( 77,268)( 78,267)( 79,266)( 80,265)
( 81,279)( 82,280)( 83,277)( 84,278)( 85,276)( 86,275)( 87,274)( 88,273)
( 89,287)( 90,288)( 91,285)( 92,286)( 93,284)( 94,283)( 95,282)( 96,281)
( 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)
( 49,169)( 50,170)( 51,172)( 52,171)( 53,175)( 54,176)( 55,173)( 56,174)
( 57,185)( 58,186)( 59,188)( 60,187)( 61,191)( 62,192)( 63,189)( 64,190)
( 65,177)( 66,178)( 67,180)( 68,179)( 69,183)( 70,184)( 71,181)( 72,182)
( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)( 79,149)( 80,150)
( 81,161)( 82,162)( 83,164)( 84,163)( 85,167)( 86,168)( 87,165)( 88,166)
( 89,153)( 90,154)( 91,156)( 92,155)( 93,159)( 94,160)( 95,157)( 96,158)
(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)
(241,362)(242,361)(243,363)(244,364)(245,368)(246,367)(247,366)(248,365)
(249,378)(250,377)(251,379)(252,380)(253,384)(254,383)(255,382)(256,381)
(257,370)(258,369)(259,371)(260,372)(261,376)(262,375)(263,374)(264,373)
(265,338)(266,337)(267,339)(268,340)(269,344)(270,343)(271,342)(272,341)
(273,354)(274,353)(275,355)(276,356)(277,360)(278,359)(279,358)(280,357)
(281,346)(282,345)(283,347)(284,348)(285,352)(286,351)(287,350)(288,349);;
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, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 49,247)( 50,248)( 51,245)( 52,246)( 53,244)( 54,243)( 55,242)
( 56,241)( 57,255)( 58,256)( 59,253)( 60,254)( 61,252)( 62,251)( 63,250)
( 64,249)( 65,263)( 66,264)( 67,261)( 68,262)( 69,260)( 70,259)( 71,258)
( 72,257)( 73,271)( 74,272)( 75,269)( 76,270)( 77,268)( 78,267)( 79,266)
( 80,265)( 81,279)( 82,280)( 83,277)( 84,278)( 85,276)( 86,275)( 87,274)
( 88,273)( 89,287)( 90,288)( 91,285)( 92,286)( 93,284)( 94,283)( 95,282)
( 96,281)( 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)( 49,169)( 50,170)( 51,172)( 52,171)( 53,175)( 54,176)( 55,173)
( 56,174)( 57,185)( 58,186)( 59,188)( 60,187)( 61,191)( 62,192)( 63,189)
( 64,190)( 65,177)( 66,178)( 67,180)( 68,179)( 69,183)( 70,184)( 71,181)
( 72,182)( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)( 79,149)
( 80,150)( 81,161)( 82,162)( 83,164)( 84,163)( 85,167)( 86,168)( 87,165)
( 88,166)( 89,153)( 90,154)( 91,156)( 92,155)( 93,159)( 94,160)( 95,157)
( 96,158)(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)(241,362)(242,361)(243,363)(244,364)(245,368)(246,367)(247,366)
(248,365)(249,378)(250,377)(251,379)(252,380)(253,384)(254,383)(255,382)
(256,381)(257,370)(258,369)(259,371)(260,372)(261,376)(262,375)(263,374)
(264,373)(265,338)(266,337)(267,339)(268,340)(269,344)(270,343)(271,342)
(272,341)(273,354)(274,353)(275,355)(276,356)(277,360)(278,359)(279,358)
(280,357)(281,346)(282,345)(283,347)(284,348)(285,352)(286,351)(287,350)
(288,349);
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, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope