Polytope of Type {4,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12}*768e
if this polytope has a name.
Group : SmallGroup(768,1087779)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 32, 192, 96
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 : {4,12}*384d, {4,12}*384e, {4,6}*384b
4-fold quotients : {4,12}*192b, {4,6}*192b, {4,12}*192c
8-fold quotients : {4,12}*96a, {4,12}*96b, {4,12}*96c, {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)
( 25,224)( 26,223)( 27,222)( 28,221)( 29,219)( 30,220)( 31,217)( 32,218)
( 33,232)( 34,231)( 35,230)( 36,229)( 37,227)( 38,228)( 39,225)( 40,226)
( 41,240)( 42,239)( 43,238)( 44,237)( 45,235)( 46,236)( 47,233)( 48,234)
( 49,248)( 50,247)( 51,246)( 52,245)( 53,243)( 54,244)( 55,241)( 56,242)
( 57,256)( 58,255)( 59,254)( 60,253)( 61,251)( 62,252)( 63,249)( 64,250)
( 65,264)( 66,263)( 67,262)( 68,261)( 69,259)( 70,260)( 71,257)( 72,258)
( 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)
(121,368)(122,367)(123,366)(124,365)(125,363)(126,364)(127,361)(128,362)
(129,376)(130,375)(131,374)(132,373)(133,371)(134,372)(135,369)(136,370)
(137,384)(138,383)(139,382)(140,381)(141,379)(142,380)(143,377)(144,378)
(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)
(169,320)(170,319)(171,318)(172,317)(173,315)(174,316)(175,313)(176,314)
(177,328)(178,327)(179,326)(180,325)(181,323)(182,324)(183,321)(184,322)
(185,336)(186,335)(187,334)(188,333)(189,331)(190,332)(191,329)(192,330);;
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)
( 49,170)( 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)
(193,313)(194,314)(195,316)(196,315)(197,319)(198,320)(199,317)(200,318)
(201,329)(202,330)(203,332)(204,331)(205,335)(206,336)(207,333)(208,334)
(209,321)(210,322)(211,324)(212,323)(213,327)(214,328)(215,325)(216,326)
(217,289)(218,290)(219,292)(220,291)(221,295)(222,296)(223,293)(224,294)
(225,305)(226,306)(227,308)(228,307)(229,311)(230,312)(231,309)(232,310)
(233,297)(234,298)(235,300)(236,299)(237,303)(238,304)(239,301)(240,302)
(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 := ( 1,234)( 2,233)( 3,237)( 4,238)( 5,235)( 6,236)( 7,239)( 8,240)
( 9,226)( 10,225)( 11,229)( 12,230)( 13,227)( 14,228)( 15,231)( 16,232)
( 17,218)( 18,217)( 19,221)( 20,222)( 21,219)( 22,220)( 23,223)( 24,224)
( 25,209)( 26,210)( 27,214)( 28,213)( 29,212)( 30,211)( 31,216)( 32,215)
( 33,201)( 34,202)( 35,206)( 36,205)( 37,204)( 38,203)( 39,208)( 40,207)
( 41,193)( 42,194)( 43,198)( 44,197)( 45,196)( 46,195)( 47,200)( 48,199)
( 49,282)( 50,281)( 51,285)( 52,286)( 53,283)( 54,284)( 55,287)( 56,288)
( 57,274)( 58,273)( 59,277)( 60,278)( 61,275)( 62,276)( 63,279)( 64,280)
( 65,266)( 66,265)( 67,269)( 68,270)( 69,267)( 70,268)( 71,271)( 72,272)
( 73,257)( 74,258)( 75,262)( 76,261)( 77,260)( 78,259)( 79,264)( 80,263)
( 81,249)( 82,250)( 83,254)( 84,253)( 85,252)( 86,251)( 87,256)( 88,255)
( 89,241)( 90,242)( 91,246)( 92,245)( 93,244)( 94,243)( 95,248)( 96,247)
( 97,354)( 98,353)( 99,357)(100,358)(101,355)(102,356)(103,359)(104,360)
(105,346)(106,345)(107,349)(108,350)(109,347)(110,348)(111,351)(112,352)
(113,338)(114,337)(115,341)(116,342)(117,339)(118,340)(119,343)(120,344)
(121,378)(122,377)(123,381)(124,382)(125,379)(126,380)(127,383)(128,384)
(129,370)(130,369)(131,373)(132,374)(133,371)(134,372)(135,375)(136,376)
(137,362)(138,361)(139,365)(140,366)(141,363)(142,364)(143,367)(144,368)
(145,305)(146,306)(147,310)(148,309)(149,308)(150,307)(151,312)(152,311)
(153,297)(154,298)(155,302)(156,301)(157,300)(158,299)(159,304)(160,303)
(161,289)(162,290)(163,294)(164,293)(165,292)(166,291)(167,296)(168,295)
(169,329)(170,330)(171,334)(172,333)(173,332)(174,331)(175,336)(176,335)
(177,321)(178,322)(179,326)(180,325)(181,324)(182,323)(183,328)(184,327)
(185,313)(186,314)(187,318)(188,317)(189,316)(190,315)(191,320)(192,319);;
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,
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*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)( 25,224)( 26,223)( 27,222)( 28,221)( 29,219)( 30,220)( 31,217)
( 32,218)( 33,232)( 34,231)( 35,230)( 36,229)( 37,227)( 38,228)( 39,225)
( 40,226)( 41,240)( 42,239)( 43,238)( 44,237)( 45,235)( 46,236)( 47,233)
( 48,234)( 49,248)( 50,247)( 51,246)( 52,245)( 53,243)( 54,244)( 55,241)
( 56,242)( 57,256)( 58,255)( 59,254)( 60,253)( 61,251)( 62,252)( 63,249)
( 64,250)( 65,264)( 66,263)( 67,262)( 68,261)( 69,259)( 70,260)( 71,257)
( 72,258)( 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)(121,368)(122,367)(123,366)(124,365)(125,363)(126,364)(127,361)
(128,362)(129,376)(130,375)(131,374)(132,373)(133,371)(134,372)(135,369)
(136,370)(137,384)(138,383)(139,382)(140,381)(141,379)(142,380)(143,377)
(144,378)(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)(169,320)(170,319)(171,318)(172,317)(173,315)(174,316)(175,313)
(176,314)(177,328)(178,327)(179,326)(180,325)(181,323)(182,324)(183,321)
(184,322)(185,336)(186,335)(187,334)(188,333)(189,331)(190,332)(191,329)
(192,330);
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)( 49,170)( 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)(193,313)(194,314)(195,316)(196,315)(197,319)(198,320)(199,317)
(200,318)(201,329)(202,330)(203,332)(204,331)(205,335)(206,336)(207,333)
(208,334)(209,321)(210,322)(211,324)(212,323)(213,327)(214,328)(215,325)
(216,326)(217,289)(218,290)(219,292)(220,291)(221,295)(222,296)(223,293)
(224,294)(225,305)(226,306)(227,308)(228,307)(229,311)(230,312)(231,309)
(232,310)(233,297)(234,298)(235,300)(236,299)(237,303)(238,304)(239,301)
(240,302)(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)!( 1,234)( 2,233)( 3,237)( 4,238)( 5,235)( 6,236)( 7,239)
( 8,240)( 9,226)( 10,225)( 11,229)( 12,230)( 13,227)( 14,228)( 15,231)
( 16,232)( 17,218)( 18,217)( 19,221)( 20,222)( 21,219)( 22,220)( 23,223)
( 24,224)( 25,209)( 26,210)( 27,214)( 28,213)( 29,212)( 30,211)( 31,216)
( 32,215)( 33,201)( 34,202)( 35,206)( 36,205)( 37,204)( 38,203)( 39,208)
( 40,207)( 41,193)( 42,194)( 43,198)( 44,197)( 45,196)( 46,195)( 47,200)
( 48,199)( 49,282)( 50,281)( 51,285)( 52,286)( 53,283)( 54,284)( 55,287)
( 56,288)( 57,274)( 58,273)( 59,277)( 60,278)( 61,275)( 62,276)( 63,279)
( 64,280)( 65,266)( 66,265)( 67,269)( 68,270)( 69,267)( 70,268)( 71,271)
( 72,272)( 73,257)( 74,258)( 75,262)( 76,261)( 77,260)( 78,259)( 79,264)
( 80,263)( 81,249)( 82,250)( 83,254)( 84,253)( 85,252)( 86,251)( 87,256)
( 88,255)( 89,241)( 90,242)( 91,246)( 92,245)( 93,244)( 94,243)( 95,248)
( 96,247)( 97,354)( 98,353)( 99,357)(100,358)(101,355)(102,356)(103,359)
(104,360)(105,346)(106,345)(107,349)(108,350)(109,347)(110,348)(111,351)
(112,352)(113,338)(114,337)(115,341)(116,342)(117,339)(118,340)(119,343)
(120,344)(121,378)(122,377)(123,381)(124,382)(125,379)(126,380)(127,383)
(128,384)(129,370)(130,369)(131,373)(132,374)(133,371)(134,372)(135,375)
(136,376)(137,362)(138,361)(139,365)(140,366)(141,363)(142,364)(143,367)
(144,368)(145,305)(146,306)(147,310)(148,309)(149,308)(150,307)(151,312)
(152,311)(153,297)(154,298)(155,302)(156,301)(157,300)(158,299)(159,304)
(160,303)(161,289)(162,290)(163,294)(164,293)(165,292)(166,291)(167,296)
(168,295)(169,329)(170,330)(171,334)(172,333)(173,332)(174,331)(175,336)
(176,335)(177,321)(178,322)(179,326)(180,325)(181,324)(182,323)(183,328)
(184,327)(185,313)(186,314)(187,318)(188,317)(189,316)(190,315)(191,320)
(192,319);
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,
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*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