Polytope of Type {8,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,156074)
Rank : 4
Schlafli Type : {8,12,3}
Number of vertices, edges, etc : 8, 96, 36, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {4,12,3}*576
3-fold quotients : {8,4,3}*384
4-fold quotients : {8,6,3}*288, {2,12,3}*288
6-fold quotients : {4,4,3}*192b
8-fold quotients : {4,6,3}*144
12-fold quotients : {8,2,3}*96, {2,4,3}*96
16-fold quotients : {2,6,3}*72
24-fold quotients : {4,2,3}*48, {2,4,3}*48
48-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)( 8,152)
( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)
( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)
( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 73,253)( 74,254)( 75,255)( 76,256)( 77,257)( 78,258)( 79,259)( 80,260)
( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)( 88,268)
( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)( 96,276)
( 97,277)( 98,278)( 99,279)(100,280)(101,281)(102,282)(103,283)(104,284)
(105,285)(106,286)(107,287)(108,288)(109,217)(110,218)(111,219)(112,220)
(113,221)(114,222)(115,223)(116,224)(117,225)(118,226)(119,227)(120,228)
(121,229)(122,230)(123,231)(124,232)(125,233)(126,234)(127,235)(128,236)
(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)(136,244)
(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,251)(144,252);;
s1 := ( 1, 3)( 2, 4)( 5, 11)( 6, 12)( 7, 9)( 8, 10)( 13, 15)( 14, 16)
( 17, 23)( 18, 24)( 19, 21)( 20, 22)( 25, 27)( 26, 28)( 29, 35)( 30, 36)
( 31, 33)( 32, 34)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)
( 49, 51)( 50, 52)( 53, 59)( 54, 60)( 55, 57)( 56, 58)( 61, 63)( 62, 64)
( 65, 71)( 66, 72)( 67, 69)( 68, 70)( 73,111)( 74,112)( 75,109)( 76,110)
( 77,119)( 78,120)( 79,117)( 80,118)( 81,115)( 82,116)( 83,113)( 84,114)
( 85,123)( 86,124)( 87,121)( 88,122)( 89,131)( 90,132)( 91,129)( 92,130)
( 93,127)( 94,128)( 95,125)( 96,126)( 97,135)( 98,136)( 99,133)(100,134)
(101,143)(102,144)(103,141)(104,142)(105,139)(106,140)(107,137)(108,138)
(145,219)(146,220)(147,217)(148,218)(149,227)(150,228)(151,225)(152,226)
(153,223)(154,224)(155,221)(156,222)(157,231)(158,232)(159,229)(160,230)
(161,239)(162,240)(163,237)(164,238)(165,235)(166,236)(167,233)(168,234)
(169,243)(170,244)(171,241)(172,242)(173,251)(174,252)(175,249)(176,250)
(177,247)(178,248)(179,245)(180,246)(181,255)(182,256)(183,253)(184,254)
(185,263)(186,264)(187,261)(188,262)(189,259)(190,260)(191,257)(192,258)
(193,267)(194,268)(195,265)(196,266)(197,275)(198,276)(199,273)(200,274)
(201,271)(202,272)(203,269)(204,270)(205,279)(206,280)(207,277)(208,278)
(209,287)(210,288)(211,285)(212,286)(213,283)(214,284)(215,281)(216,282);;
s2 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 13, 29)( 14, 30)( 15, 32)
( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)( 23, 36)
( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)( 50, 66)
( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)( 58, 70)
( 59, 72)( 60, 71)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 83, 84)( 85,101)
( 86,102)( 87,104)( 88,103)( 89, 97)( 90, 98)( 91,100)( 92, 99)( 93,105)
( 94,106)( 95,108)( 96,107)(109,113)(110,114)(111,116)(112,115)(119,120)
(121,137)(122,138)(123,140)(124,139)(125,133)(126,134)(127,136)(128,135)
(129,141)(130,142)(131,144)(132,143)(145,149)(146,150)(147,152)(148,151)
(155,156)(157,173)(158,174)(159,176)(160,175)(161,169)(162,170)(163,172)
(164,171)(165,177)(166,178)(167,180)(168,179)(181,185)(182,186)(183,188)
(184,187)(191,192)(193,209)(194,210)(195,212)(196,211)(197,205)(198,206)
(199,208)(200,207)(201,213)(202,214)(203,216)(204,215)(217,221)(218,222)
(219,224)(220,223)(227,228)(229,245)(230,246)(231,248)(232,247)(233,241)
(234,242)(235,244)(236,243)(237,249)(238,250)(239,252)(240,251)(253,257)
(254,258)(255,260)(256,259)(263,264)(265,281)(266,282)(267,284)(268,283)
(269,277)(270,278)(271,280)(272,279)(273,285)(274,286)(275,288)(276,287);;
s3 := ( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 21)( 6, 24)( 7, 23)( 8, 22)
( 9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)( 31, 35)
( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)( 43, 59)
( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)( 66, 72)
( 67, 71)( 68, 70)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)( 78, 96)
( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 98,100)(101,105)
(102,108)(103,107)(104,106)(109,121)(110,124)(111,123)(112,122)(113,129)
(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)(134,136)
(137,141)(138,144)(139,143)(140,142)(145,157)(146,160)(147,159)(148,158)
(149,165)(150,168)(151,167)(152,166)(153,161)(154,164)(155,163)(156,162)
(170,172)(173,177)(174,180)(175,179)(176,178)(181,193)(182,196)(183,195)
(184,194)(185,201)(186,204)(187,203)(188,202)(189,197)(190,200)(191,199)
(192,198)(206,208)(209,213)(210,216)(211,215)(212,214)(217,229)(218,232)
(219,231)(220,230)(221,237)(222,240)(223,239)(224,238)(225,233)(226,236)
(227,235)(228,234)(242,244)(245,249)(246,252)(247,251)(248,250)(253,265)
(254,268)(255,267)(256,266)(257,273)(258,276)(259,275)(260,274)(261,269)
(262,272)(263,271)(264,270)(278,280)(281,285)(282,288)(283,287)(284,286);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)
( 8,152)( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)
( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)
( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)
( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 73,253)( 74,254)( 75,255)( 76,256)( 77,257)( 78,258)( 79,259)
( 80,260)( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)
( 88,268)( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)
( 96,276)( 97,277)( 98,278)( 99,279)(100,280)(101,281)(102,282)(103,283)
(104,284)(105,285)(106,286)(107,287)(108,288)(109,217)(110,218)(111,219)
(112,220)(113,221)(114,222)(115,223)(116,224)(117,225)(118,226)(119,227)
(120,228)(121,229)(122,230)(123,231)(124,232)(125,233)(126,234)(127,235)
(128,236)(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)
(136,244)(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,251)
(144,252);
s1 := Sym(288)!( 1, 3)( 2, 4)( 5, 11)( 6, 12)( 7, 9)( 8, 10)( 13, 15)
( 14, 16)( 17, 23)( 18, 24)( 19, 21)( 20, 22)( 25, 27)( 26, 28)( 29, 35)
( 30, 36)( 31, 33)( 32, 34)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)
( 44, 46)( 49, 51)( 50, 52)( 53, 59)( 54, 60)( 55, 57)( 56, 58)( 61, 63)
( 62, 64)( 65, 71)( 66, 72)( 67, 69)( 68, 70)( 73,111)( 74,112)( 75,109)
( 76,110)( 77,119)( 78,120)( 79,117)( 80,118)( 81,115)( 82,116)( 83,113)
( 84,114)( 85,123)( 86,124)( 87,121)( 88,122)( 89,131)( 90,132)( 91,129)
( 92,130)( 93,127)( 94,128)( 95,125)( 96,126)( 97,135)( 98,136)( 99,133)
(100,134)(101,143)(102,144)(103,141)(104,142)(105,139)(106,140)(107,137)
(108,138)(145,219)(146,220)(147,217)(148,218)(149,227)(150,228)(151,225)
(152,226)(153,223)(154,224)(155,221)(156,222)(157,231)(158,232)(159,229)
(160,230)(161,239)(162,240)(163,237)(164,238)(165,235)(166,236)(167,233)
(168,234)(169,243)(170,244)(171,241)(172,242)(173,251)(174,252)(175,249)
(176,250)(177,247)(178,248)(179,245)(180,246)(181,255)(182,256)(183,253)
(184,254)(185,263)(186,264)(187,261)(188,262)(189,259)(190,260)(191,257)
(192,258)(193,267)(194,268)(195,265)(196,266)(197,275)(198,276)(199,273)
(200,274)(201,271)(202,272)(203,269)(204,270)(205,279)(206,280)(207,277)
(208,278)(209,287)(210,288)(211,285)(212,286)(213,283)(214,284)(215,281)
(216,282);
s2 := Sym(288)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 13, 29)( 14, 30)
( 15, 32)( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)
( 23, 36)( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)
( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)
( 58, 70)( 59, 72)( 60, 71)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 83, 84)
( 85,101)( 86,102)( 87,104)( 88,103)( 89, 97)( 90, 98)( 91,100)( 92, 99)
( 93,105)( 94,106)( 95,108)( 96,107)(109,113)(110,114)(111,116)(112,115)
(119,120)(121,137)(122,138)(123,140)(124,139)(125,133)(126,134)(127,136)
(128,135)(129,141)(130,142)(131,144)(132,143)(145,149)(146,150)(147,152)
(148,151)(155,156)(157,173)(158,174)(159,176)(160,175)(161,169)(162,170)
(163,172)(164,171)(165,177)(166,178)(167,180)(168,179)(181,185)(182,186)
(183,188)(184,187)(191,192)(193,209)(194,210)(195,212)(196,211)(197,205)
(198,206)(199,208)(200,207)(201,213)(202,214)(203,216)(204,215)(217,221)
(218,222)(219,224)(220,223)(227,228)(229,245)(230,246)(231,248)(232,247)
(233,241)(234,242)(235,244)(236,243)(237,249)(238,250)(239,252)(240,251)
(253,257)(254,258)(255,260)(256,259)(263,264)(265,281)(266,282)(267,284)
(268,283)(269,277)(270,278)(271,280)(272,279)(273,285)(274,286)(275,288)
(276,287);
s3 := Sym(288)!( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 21)( 6, 24)( 7, 23)
( 8, 22)( 9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)
( 31, 35)( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)
( 43, 59)( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)
( 66, 72)( 67, 71)( 68, 70)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)
( 78, 96)( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 98,100)
(101,105)(102,108)(103,107)(104,106)(109,121)(110,124)(111,123)(112,122)
(113,129)(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)
(134,136)(137,141)(138,144)(139,143)(140,142)(145,157)(146,160)(147,159)
(148,158)(149,165)(150,168)(151,167)(152,166)(153,161)(154,164)(155,163)
(156,162)(170,172)(173,177)(174,180)(175,179)(176,178)(181,193)(182,196)
(183,195)(184,194)(185,201)(186,204)(187,203)(188,202)(189,197)(190,200)
(191,199)(192,198)(206,208)(209,213)(210,216)(211,215)(212,214)(217,229)
(218,232)(219,231)(220,230)(221,237)(222,240)(223,239)(224,238)(225,233)
(226,236)(227,235)(228,234)(242,244)(245,249)(246,252)(247,251)(248,250)
(253,265)(254,268)(255,267)(256,266)(257,273)(258,276)(259,275)(260,274)
(261,269)(262,272)(263,271)(264,270)(278,280)(281,285)(282,288)(283,287)
(284,286);
poly := sub<Sym(288)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 >;
References : None.
to this polytope