Polytope of Type {12,32}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,32}*768a
Also Known As : {12,32|2}. if this polytope has another name.
Group : SmallGroup(768,90208)
Rank : 3
Schlafli Type : {12,32}
Number of vertices, edges, etc : 12, 192, 32
Order of s0s1s2 : 96
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {12,16}*384a, {6,32}*384
3-fold quotients : {4,32}*256a
4-fold quotients : {12,8}*192a, {6,16}*192
6-fold quotients : {4,16}*128a, {2,32}*128
8-fold quotients : {12,4}*96a, {6,8}*96
12-fold quotients : {4,8}*64a, {2,16}*64
16-fold quotients : {12,2}*48, {6,4}*48a
24-fold quotients : {4,4}*32, {2,8}*32
32-fold quotients : {6,2}*24
48-fold quotients : {2,4}*16, {4,2}*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 := ( 1, 97)( 2, 99)( 3, 98)( 4,100)( 5,102)( 6,101)( 7,103)( 8,105)
( 9,104)( 10,106)( 11,108)( 12,107)( 13,109)( 14,111)( 15,110)( 16,112)
( 17,114)( 18,113)( 19,115)( 20,117)( 21,116)( 22,118)( 23,120)( 24,119)
( 25,121)( 26,123)( 27,122)( 28,124)( 29,126)( 30,125)( 31,127)( 32,129)
( 33,128)( 34,130)( 35,132)( 36,131)( 37,133)( 38,135)( 39,134)( 40,136)
( 41,138)( 42,137)( 43,139)( 44,141)( 45,140)( 46,142)( 47,144)( 48,143)
( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)( 56,153)
( 57,152)( 58,154)( 59,156)( 60,155)( 61,157)( 62,159)( 63,158)( 64,160)
( 65,162)( 66,161)( 67,163)( 68,165)( 69,164)( 70,166)( 71,168)( 72,167)
( 73,169)( 74,171)( 75,170)( 76,172)( 77,174)( 78,173)( 79,175)( 80,177)
( 81,176)( 82,178)( 83,180)( 84,179)( 85,181)( 86,183)( 87,182)( 88,184)
( 89,186)( 90,185)( 91,187)( 92,189)( 93,188)( 94,190)( 95,192)( 96,191)
(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,295)(200,297)
(201,296)(202,298)(203,300)(204,299)(205,301)(206,303)(207,302)(208,304)
(209,306)(210,305)(211,307)(212,309)(213,308)(214,310)(215,312)(216,311)
(217,313)(218,315)(219,314)(220,316)(221,318)(222,317)(223,319)(224,321)
(225,320)(226,322)(227,324)(228,323)(229,325)(230,327)(231,326)(232,328)
(233,330)(234,329)(235,331)(236,333)(237,332)(238,334)(239,336)(240,335)
(241,337)(242,339)(243,338)(244,340)(245,342)(246,341)(247,343)(248,345)
(249,344)(250,346)(251,348)(252,347)(253,349)(254,351)(255,350)(256,352)
(257,354)(258,353)(259,355)(260,357)(261,356)(262,358)(263,360)(264,359)
(265,361)(266,363)(267,362)(268,364)(269,366)(270,365)(271,367)(272,369)
(273,368)(274,370)(275,372)(276,371)(277,373)(278,375)(279,374)(280,376)
(281,378)(282,377)(283,379)(284,381)(285,380)(286,382)(287,384)(288,383);;
s1 := ( 1, 3)( 4, 6)( 7, 12)( 8, 11)( 9, 10)( 13, 21)( 14, 20)( 15, 19)
( 16, 24)( 17, 23)( 18, 22)( 25, 27)( 28, 30)( 31, 36)( 32, 35)( 33, 34)
( 37, 45)( 38, 44)( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 49, 63)( 50, 62)
( 51, 61)( 52, 66)( 53, 65)( 54, 64)( 55, 72)( 56, 71)( 57, 70)( 58, 69)
( 59, 68)( 60, 67)( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)
( 79, 96)( 80, 95)( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 97,123)( 98,122)
( 99,121)(100,126)(101,125)(102,124)(103,132)(104,131)(105,130)(106,129)
(107,128)(108,127)(109,141)(110,140)(111,139)(112,144)(113,143)(114,142)
(115,135)(116,134)(117,133)(118,138)(119,137)(120,136)(145,183)(146,182)
(147,181)(148,186)(149,185)(150,184)(151,192)(152,191)(153,190)(154,189)
(155,188)(156,187)(157,171)(158,170)(159,169)(160,174)(161,173)(162,172)
(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(193,243)(194,242)
(195,241)(196,246)(197,245)(198,244)(199,252)(200,251)(201,250)(202,249)
(203,248)(204,247)(205,261)(206,260)(207,259)(208,264)(209,263)(210,262)
(211,255)(212,254)(213,253)(214,258)(215,257)(216,256)(217,267)(218,266)
(219,265)(220,270)(221,269)(222,268)(223,276)(224,275)(225,274)(226,273)
(227,272)(228,271)(229,285)(230,284)(231,283)(232,288)(233,287)(234,286)
(235,279)(236,278)(237,277)(238,282)(239,281)(240,280)(289,363)(290,362)
(291,361)(292,366)(293,365)(294,364)(295,372)(296,371)(297,370)(298,369)
(299,368)(300,367)(301,381)(302,380)(303,379)(304,384)(305,383)(306,382)
(307,375)(308,374)(309,373)(310,378)(311,377)(312,376)(313,339)(314,338)
(315,337)(316,342)(317,341)(318,340)(319,348)(320,347)(321,346)(322,345)
(323,344)(324,343)(325,357)(326,356)(327,355)(328,360)(329,359)(330,358)
(331,351)(332,350)(333,349)(334,354)(335,353)(336,352);;
s2 := ( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,202)( 8,203)
( 9,204)( 10,199)( 11,200)( 12,201)( 13,211)( 14,212)( 15,213)( 16,214)
( 17,215)( 18,216)( 19,205)( 20,206)( 21,207)( 22,208)( 23,209)( 24,210)
( 25,217)( 26,218)( 27,219)( 28,220)( 29,221)( 30,222)( 31,226)( 32,227)
( 33,228)( 34,223)( 35,224)( 36,225)( 37,235)( 38,236)( 39,237)( 40,238)
( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)( 48,234)
( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,262)( 56,263)
( 57,264)( 58,259)( 59,260)( 60,261)( 61,241)( 62,242)( 63,243)( 64,244)
( 65,245)( 66,246)( 67,250)( 68,251)( 69,252)( 70,247)( 71,248)( 72,249)
( 73,277)( 74,278)( 75,279)( 76,280)( 77,281)( 78,282)( 79,286)( 80,287)
( 81,288)( 82,283)( 83,284)( 84,285)( 85,265)( 86,266)( 87,267)( 88,268)
( 89,269)( 90,270)( 91,274)( 92,275)( 93,276)( 94,271)( 95,272)( 96,273)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)(104,299)
(105,300)(106,295)(107,296)(108,297)(109,307)(110,308)(111,309)(112,310)
(113,311)(114,312)(115,301)(116,302)(117,303)(118,304)(119,305)(120,306)
(121,313)(122,314)(123,315)(124,316)(125,317)(126,318)(127,322)(128,323)
(129,324)(130,319)(131,320)(132,321)(133,331)(134,332)(135,333)(136,334)
(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)(144,330)
(145,349)(146,350)(147,351)(148,352)(149,353)(150,354)(151,358)(152,359)
(153,360)(154,355)(155,356)(156,357)(157,337)(158,338)(159,339)(160,340)
(161,341)(162,342)(163,346)(164,347)(165,348)(166,343)(167,344)(168,345)
(169,373)(170,374)(171,375)(172,376)(173,377)(174,378)(175,382)(176,383)
(177,384)(178,379)(179,380)(180,381)(181,361)(182,362)(183,363)(184,364)
(185,365)(186,366)(187,370)(188,371)(189,372)(190,367)(191,368)(192,369);;
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*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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, 97)( 2, 99)( 3, 98)( 4,100)( 5,102)( 6,101)( 7,103)
( 8,105)( 9,104)( 10,106)( 11,108)( 12,107)( 13,109)( 14,111)( 15,110)
( 16,112)( 17,114)( 18,113)( 19,115)( 20,117)( 21,116)( 22,118)( 23,120)
( 24,119)( 25,121)( 26,123)( 27,122)( 28,124)( 29,126)( 30,125)( 31,127)
( 32,129)( 33,128)( 34,130)( 35,132)( 36,131)( 37,133)( 38,135)( 39,134)
( 40,136)( 41,138)( 42,137)( 43,139)( 44,141)( 45,140)( 46,142)( 47,144)
( 48,143)( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)
( 56,153)( 57,152)( 58,154)( 59,156)( 60,155)( 61,157)( 62,159)( 63,158)
( 64,160)( 65,162)( 66,161)( 67,163)( 68,165)( 69,164)( 70,166)( 71,168)
( 72,167)( 73,169)( 74,171)( 75,170)( 76,172)( 77,174)( 78,173)( 79,175)
( 80,177)( 81,176)( 82,178)( 83,180)( 84,179)( 85,181)( 86,183)( 87,182)
( 88,184)( 89,186)( 90,185)( 91,187)( 92,189)( 93,188)( 94,190)( 95,192)
( 96,191)(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,295)
(200,297)(201,296)(202,298)(203,300)(204,299)(205,301)(206,303)(207,302)
(208,304)(209,306)(210,305)(211,307)(212,309)(213,308)(214,310)(215,312)
(216,311)(217,313)(218,315)(219,314)(220,316)(221,318)(222,317)(223,319)
(224,321)(225,320)(226,322)(227,324)(228,323)(229,325)(230,327)(231,326)
(232,328)(233,330)(234,329)(235,331)(236,333)(237,332)(238,334)(239,336)
(240,335)(241,337)(242,339)(243,338)(244,340)(245,342)(246,341)(247,343)
(248,345)(249,344)(250,346)(251,348)(252,347)(253,349)(254,351)(255,350)
(256,352)(257,354)(258,353)(259,355)(260,357)(261,356)(262,358)(263,360)
(264,359)(265,361)(266,363)(267,362)(268,364)(269,366)(270,365)(271,367)
(272,369)(273,368)(274,370)(275,372)(276,371)(277,373)(278,375)(279,374)
(280,376)(281,378)(282,377)(283,379)(284,381)(285,380)(286,382)(287,384)
(288,383);
s1 := Sym(384)!( 1, 3)( 4, 6)( 7, 12)( 8, 11)( 9, 10)( 13, 21)( 14, 20)
( 15, 19)( 16, 24)( 17, 23)( 18, 22)( 25, 27)( 28, 30)( 31, 36)( 32, 35)
( 33, 34)( 37, 45)( 38, 44)( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 49, 63)
( 50, 62)( 51, 61)( 52, 66)( 53, 65)( 54, 64)( 55, 72)( 56, 71)( 57, 70)
( 58, 69)( 59, 68)( 60, 67)( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)
( 78, 88)( 79, 96)( 80, 95)( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 97,123)
( 98,122)( 99,121)(100,126)(101,125)(102,124)(103,132)(104,131)(105,130)
(106,129)(107,128)(108,127)(109,141)(110,140)(111,139)(112,144)(113,143)
(114,142)(115,135)(116,134)(117,133)(118,138)(119,137)(120,136)(145,183)
(146,182)(147,181)(148,186)(149,185)(150,184)(151,192)(152,191)(153,190)
(154,189)(155,188)(156,187)(157,171)(158,170)(159,169)(160,174)(161,173)
(162,172)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(193,243)
(194,242)(195,241)(196,246)(197,245)(198,244)(199,252)(200,251)(201,250)
(202,249)(203,248)(204,247)(205,261)(206,260)(207,259)(208,264)(209,263)
(210,262)(211,255)(212,254)(213,253)(214,258)(215,257)(216,256)(217,267)
(218,266)(219,265)(220,270)(221,269)(222,268)(223,276)(224,275)(225,274)
(226,273)(227,272)(228,271)(229,285)(230,284)(231,283)(232,288)(233,287)
(234,286)(235,279)(236,278)(237,277)(238,282)(239,281)(240,280)(289,363)
(290,362)(291,361)(292,366)(293,365)(294,364)(295,372)(296,371)(297,370)
(298,369)(299,368)(300,367)(301,381)(302,380)(303,379)(304,384)(305,383)
(306,382)(307,375)(308,374)(309,373)(310,378)(311,377)(312,376)(313,339)
(314,338)(315,337)(316,342)(317,341)(318,340)(319,348)(320,347)(321,346)
(322,345)(323,344)(324,343)(325,357)(326,356)(327,355)(328,360)(329,359)
(330,358)(331,351)(332,350)(333,349)(334,354)(335,353)(336,352);
s2 := Sym(384)!( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,202)
( 8,203)( 9,204)( 10,199)( 11,200)( 12,201)( 13,211)( 14,212)( 15,213)
( 16,214)( 17,215)( 18,216)( 19,205)( 20,206)( 21,207)( 22,208)( 23,209)
( 24,210)( 25,217)( 26,218)( 27,219)( 28,220)( 29,221)( 30,222)( 31,226)
( 32,227)( 33,228)( 34,223)( 35,224)( 36,225)( 37,235)( 38,236)( 39,237)
( 40,238)( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)
( 48,234)( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,262)
( 56,263)( 57,264)( 58,259)( 59,260)( 60,261)( 61,241)( 62,242)( 63,243)
( 64,244)( 65,245)( 66,246)( 67,250)( 68,251)( 69,252)( 70,247)( 71,248)
( 72,249)( 73,277)( 74,278)( 75,279)( 76,280)( 77,281)( 78,282)( 79,286)
( 80,287)( 81,288)( 82,283)( 83,284)( 84,285)( 85,265)( 86,266)( 87,267)
( 88,268)( 89,269)( 90,270)( 91,274)( 92,275)( 93,276)( 94,271)( 95,272)
( 96,273)( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)
(104,299)(105,300)(106,295)(107,296)(108,297)(109,307)(110,308)(111,309)
(112,310)(113,311)(114,312)(115,301)(116,302)(117,303)(118,304)(119,305)
(120,306)(121,313)(122,314)(123,315)(124,316)(125,317)(126,318)(127,322)
(128,323)(129,324)(130,319)(131,320)(132,321)(133,331)(134,332)(135,333)
(136,334)(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)
(144,330)(145,349)(146,350)(147,351)(148,352)(149,353)(150,354)(151,358)
(152,359)(153,360)(154,355)(155,356)(156,357)(157,337)(158,338)(159,339)
(160,340)(161,341)(162,342)(163,346)(164,347)(165,348)(166,343)(167,344)
(168,345)(169,373)(170,374)(171,375)(172,376)(173,377)(174,378)(175,382)
(176,383)(177,384)(178,379)(179,380)(180,381)(181,361)(182,362)(183,363)
(184,364)(185,365)(186,366)(187,370)(188,371)(189,372)(190,367)(191,368)
(192,369);
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*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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