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