Polytope of Type {2,8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98809)
Rank : 4
Schlafli Type : {2,8,12}
Number of vertices, edges, etc : 2, 24, 144, 36
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
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 : {2,4,12}*576
4-fold quotients : {2,4,6}*288
8-fold quotients : {2,4,6}*144
9-fold quotients : {2,8,4}*128b
18-fold quotients : {2,4,4}*64
36-fold quotients : {2,2,4}*32, {2,4,2}*32
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 6, 9)( 7, 10)( 8, 11)( 15, 18)( 16, 19)( 17, 20)( 21, 30)( 22, 31)
( 23, 32)( 24, 36)( 25, 37)( 26, 38)( 27, 33)( 28, 34)( 29, 35)( 39, 48)
( 40, 49)( 41, 50)( 42, 54)( 43, 55)( 44, 56)( 45, 51)( 46, 52)( 47, 53)
( 60, 63)( 61, 64)( 62, 65)( 69, 72)( 70, 73)( 71, 74)( 78, 81)( 79, 82)
( 80, 83)( 87, 90)( 88, 91)( 89, 92)( 93,102)( 94,103)( 95,104)( 96,108)
( 97,109)( 98,110)( 99,105)(100,106)(101,107)(111,120)(112,121)(113,122)
(114,126)(115,127)(116,128)(117,123)(118,124)(119,125)(132,135)(133,136)
(134,137)(141,144)(142,145)(143,146)(147,183)(148,184)(149,185)(150,189)
(151,190)(152,191)(153,186)(154,187)(155,188)(156,192)(157,193)(158,194)
(159,198)(160,199)(161,200)(162,195)(163,196)(164,197)(165,210)(166,211)
(167,212)(168,216)(169,217)(170,218)(171,213)(172,214)(173,215)(174,201)
(175,202)(176,203)(177,207)(178,208)(179,209)(180,204)(181,205)(182,206)
(219,264)(220,265)(221,266)(222,270)(223,271)(224,272)(225,267)(226,268)
(227,269)(228,255)(229,256)(230,257)(231,261)(232,262)(233,263)(234,258)
(235,259)(236,260)(237,273)(238,274)(239,275)(240,279)(241,280)(242,281)
(243,276)(244,277)(245,278)(246,282)(247,283)(248,284)(249,288)(250,289)
(251,290)(252,285)(253,286)(254,287);;
s2 := ( 3,147)( 4,150)( 5,153)( 6,148)( 7,151)( 8,154)( 9,149)( 10,152)
( 11,155)( 12,156)( 13,159)( 14,162)( 15,157)( 16,160)( 17,163)( 18,158)
( 19,161)( 20,164)( 21,165)( 22,168)( 23,171)( 24,166)( 25,169)( 26,172)
( 27,167)( 28,170)( 29,173)( 30,174)( 31,177)( 32,180)( 33,175)( 34,178)
( 35,181)( 36,176)( 37,179)( 38,182)( 39,192)( 40,195)( 41,198)( 42,193)
( 43,196)( 44,199)( 45,194)( 46,197)( 47,200)( 48,183)( 49,186)( 50,189)
( 51,184)( 52,187)( 53,190)( 54,185)( 55,188)( 56,191)( 57,210)( 58,213)
( 59,216)( 60,211)( 61,214)( 62,217)( 63,212)( 64,215)( 65,218)( 66,201)
( 67,204)( 68,207)( 69,202)( 70,205)( 71,208)( 72,203)( 73,206)( 74,209)
( 75,237)( 76,240)( 77,243)( 78,238)( 79,241)( 80,244)( 81,239)( 82,242)
( 83,245)( 84,246)( 85,249)( 86,252)( 87,247)( 88,250)( 89,253)( 90,248)
( 91,251)( 92,254)( 93,219)( 94,222)( 95,225)( 96,220)( 97,223)( 98,226)
( 99,221)(100,224)(101,227)(102,228)(103,231)(104,234)(105,229)(106,232)
(107,235)(108,230)(109,233)(110,236)(111,282)(112,285)(113,288)(114,283)
(115,286)(116,289)(117,284)(118,287)(119,290)(120,273)(121,276)(122,279)
(123,274)(124,277)(125,280)(126,275)(127,278)(128,281)(129,264)(130,267)
(131,270)(132,265)(133,268)(134,271)(135,266)(136,269)(137,272)(138,255)
(139,258)(140,261)(141,256)(142,259)(143,262)(144,257)(145,260)(146,263);;
s3 := ( 3,130)( 4,129)( 5,131)( 6,136)( 7,135)( 8,137)( 9,133)( 10,132)
( 11,134)( 12,139)( 13,138)( 14,140)( 15,145)( 16,144)( 17,146)( 18,142)
( 19,141)( 20,143)( 21,112)( 22,111)( 23,113)( 24,118)( 25,117)( 26,119)
( 27,115)( 28,114)( 29,116)( 30,121)( 31,120)( 32,122)( 33,127)( 34,126)
( 35,128)( 36,124)( 37,123)( 38,125)( 39, 94)( 40, 93)( 41, 95)( 42,100)
( 43, 99)( 44,101)( 45, 97)( 46, 96)( 47, 98)( 48,103)( 49,102)( 50,104)
( 51,109)( 52,108)( 53,110)( 54,106)( 55,105)( 56,107)( 57, 76)( 58, 75)
( 59, 77)( 60, 82)( 61, 81)( 62, 83)( 63, 79)( 64, 78)( 65, 80)( 66, 85)
( 67, 84)( 68, 86)( 69, 91)( 70, 90)( 71, 92)( 72, 88)( 73, 87)( 74, 89)
(147,274)(148,273)(149,275)(150,280)(151,279)(152,281)(153,277)(154,276)
(155,278)(156,283)(157,282)(158,284)(159,289)(160,288)(161,290)(162,286)
(163,285)(164,287)(165,256)(166,255)(167,257)(168,262)(169,261)(170,263)
(171,259)(172,258)(173,260)(174,265)(175,264)(176,266)(177,271)(178,270)
(179,272)(180,268)(181,267)(182,269)(183,238)(184,237)(185,239)(186,244)
(187,243)(188,245)(189,241)(190,240)(191,242)(192,247)(193,246)(194,248)
(195,253)(196,252)(197,254)(198,250)(199,249)(200,251)(201,220)(202,219)
(203,221)(204,226)(205,225)(206,227)(207,223)(208,222)(209,224)(210,229)
(211,228)(212,230)(213,235)(214,234)(215,236)(216,232)(217,231)(218,233);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(290)!(1,2);
s1 := Sym(290)!( 6, 9)( 7, 10)( 8, 11)( 15, 18)( 16, 19)( 17, 20)( 21, 30)
( 22, 31)( 23, 32)( 24, 36)( 25, 37)( 26, 38)( 27, 33)( 28, 34)( 29, 35)
( 39, 48)( 40, 49)( 41, 50)( 42, 54)( 43, 55)( 44, 56)( 45, 51)( 46, 52)
( 47, 53)( 60, 63)( 61, 64)( 62, 65)( 69, 72)( 70, 73)( 71, 74)( 78, 81)
( 79, 82)( 80, 83)( 87, 90)( 88, 91)( 89, 92)( 93,102)( 94,103)( 95,104)
( 96,108)( 97,109)( 98,110)( 99,105)(100,106)(101,107)(111,120)(112,121)
(113,122)(114,126)(115,127)(116,128)(117,123)(118,124)(119,125)(132,135)
(133,136)(134,137)(141,144)(142,145)(143,146)(147,183)(148,184)(149,185)
(150,189)(151,190)(152,191)(153,186)(154,187)(155,188)(156,192)(157,193)
(158,194)(159,198)(160,199)(161,200)(162,195)(163,196)(164,197)(165,210)
(166,211)(167,212)(168,216)(169,217)(170,218)(171,213)(172,214)(173,215)
(174,201)(175,202)(176,203)(177,207)(178,208)(179,209)(180,204)(181,205)
(182,206)(219,264)(220,265)(221,266)(222,270)(223,271)(224,272)(225,267)
(226,268)(227,269)(228,255)(229,256)(230,257)(231,261)(232,262)(233,263)
(234,258)(235,259)(236,260)(237,273)(238,274)(239,275)(240,279)(241,280)
(242,281)(243,276)(244,277)(245,278)(246,282)(247,283)(248,284)(249,288)
(250,289)(251,290)(252,285)(253,286)(254,287);
s2 := Sym(290)!( 3,147)( 4,150)( 5,153)( 6,148)( 7,151)( 8,154)( 9,149)
( 10,152)( 11,155)( 12,156)( 13,159)( 14,162)( 15,157)( 16,160)( 17,163)
( 18,158)( 19,161)( 20,164)( 21,165)( 22,168)( 23,171)( 24,166)( 25,169)
( 26,172)( 27,167)( 28,170)( 29,173)( 30,174)( 31,177)( 32,180)( 33,175)
( 34,178)( 35,181)( 36,176)( 37,179)( 38,182)( 39,192)( 40,195)( 41,198)
( 42,193)( 43,196)( 44,199)( 45,194)( 46,197)( 47,200)( 48,183)( 49,186)
( 50,189)( 51,184)( 52,187)( 53,190)( 54,185)( 55,188)( 56,191)( 57,210)
( 58,213)( 59,216)( 60,211)( 61,214)( 62,217)( 63,212)( 64,215)( 65,218)
( 66,201)( 67,204)( 68,207)( 69,202)( 70,205)( 71,208)( 72,203)( 73,206)
( 74,209)( 75,237)( 76,240)( 77,243)( 78,238)( 79,241)( 80,244)( 81,239)
( 82,242)( 83,245)( 84,246)( 85,249)( 86,252)( 87,247)( 88,250)( 89,253)
( 90,248)( 91,251)( 92,254)( 93,219)( 94,222)( 95,225)( 96,220)( 97,223)
( 98,226)( 99,221)(100,224)(101,227)(102,228)(103,231)(104,234)(105,229)
(106,232)(107,235)(108,230)(109,233)(110,236)(111,282)(112,285)(113,288)
(114,283)(115,286)(116,289)(117,284)(118,287)(119,290)(120,273)(121,276)
(122,279)(123,274)(124,277)(125,280)(126,275)(127,278)(128,281)(129,264)
(130,267)(131,270)(132,265)(133,268)(134,271)(135,266)(136,269)(137,272)
(138,255)(139,258)(140,261)(141,256)(142,259)(143,262)(144,257)(145,260)
(146,263);
s3 := Sym(290)!( 3,130)( 4,129)( 5,131)( 6,136)( 7,135)( 8,137)( 9,133)
( 10,132)( 11,134)( 12,139)( 13,138)( 14,140)( 15,145)( 16,144)( 17,146)
( 18,142)( 19,141)( 20,143)( 21,112)( 22,111)( 23,113)( 24,118)( 25,117)
( 26,119)( 27,115)( 28,114)( 29,116)( 30,121)( 31,120)( 32,122)( 33,127)
( 34,126)( 35,128)( 36,124)( 37,123)( 38,125)( 39, 94)( 40, 93)( 41, 95)
( 42,100)( 43, 99)( 44,101)( 45, 97)( 46, 96)( 47, 98)( 48,103)( 49,102)
( 50,104)( 51,109)( 52,108)( 53,110)( 54,106)( 55,105)( 56,107)( 57, 76)
( 58, 75)( 59, 77)( 60, 82)( 61, 81)( 62, 83)( 63, 79)( 64, 78)( 65, 80)
( 66, 85)( 67, 84)( 68, 86)( 69, 91)( 70, 90)( 71, 92)( 72, 88)( 73, 87)
( 74, 89)(147,274)(148,273)(149,275)(150,280)(151,279)(152,281)(153,277)
(154,276)(155,278)(156,283)(157,282)(158,284)(159,289)(160,288)(161,290)
(162,286)(163,285)(164,287)(165,256)(166,255)(167,257)(168,262)(169,261)
(170,263)(171,259)(172,258)(173,260)(174,265)(175,264)(176,266)(177,271)
(178,270)(179,272)(180,268)(181,267)(182,269)(183,238)(184,237)(185,239)
(186,244)(187,243)(188,245)(189,241)(190,240)(191,242)(192,247)(193,246)
(194,248)(195,253)(196,252)(197,254)(198,250)(199,249)(200,251)(201,220)
(202,219)(203,221)(204,226)(205,225)(206,227)(207,223)(208,222)(209,224)
(210,229)(211,228)(212,230)(213,235)(214,234)(215,236)(216,232)(217,231)
(218,233);
poly := sub<Sym(290)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s3 >;
to this polytope