Polytope of Type {12,8,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,155788)
Rank : 4
Schlafli Type : {12,8,3}
Number of vertices, edges, etc : 12, 96, 24, 6
Order of s0s1s2s3 : 12
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 : {12,4,3}*576, {6,8,3}*576
3-fold quotients : {4,8,3}*384
4-fold quotients : {6,4,3}*288
6-fold quotients : {4,4,3}*192b, {2,8,3}*192
8-fold quotients : {12,2,3}*144
12-fold quotients : {2,4,3}*96
16-fold quotients : {6,2,3}*72
24-fold quotients : {4,2,3}*48, {2,4,3}*48
32-fold quotients : {3,2,3}*36
48-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)
(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)(160,240)
(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)(168,232)
(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)
(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)(184,264)
(185,249)(186,250)(187,251)(188,252)(189,253)(190,254)(191,255)(192,256)
(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)
(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)
(209,273)(210,274)(211,275)(212,276)(213,277)(214,278)(215,279)(216,280);;
s1 := ( 1,157)( 2,158)( 3,160)( 4,159)( 5,154)( 6,153)( 7,155)( 8,156)
( 9,149)( 10,150)( 11,152)( 12,151)( 13,146)( 14,145)( 15,147)( 16,148)
( 17,165)( 18,166)( 19,168)( 20,167)( 21,162)( 22,161)( 23,163)( 24,164)
( 25,181)( 26,182)( 27,184)( 28,183)( 29,178)( 30,177)( 31,179)( 32,180)
( 33,173)( 34,174)( 35,176)( 36,175)( 37,170)( 38,169)( 39,171)( 40,172)
( 41,189)( 42,190)( 43,192)( 44,191)( 45,186)( 46,185)( 47,187)( 48,188)
( 49,205)( 50,206)( 51,208)( 52,207)( 53,202)( 54,201)( 55,203)( 56,204)
( 57,197)( 58,198)( 59,200)( 60,199)( 61,194)( 62,193)( 63,195)( 64,196)
( 65,213)( 66,214)( 67,216)( 68,215)( 69,210)( 70,209)( 71,211)( 72,212)
( 73,229)( 74,230)( 75,232)( 76,231)( 77,226)( 78,225)( 79,227)( 80,228)
( 81,221)( 82,222)( 83,224)( 84,223)( 85,218)( 86,217)( 87,219)( 88,220)
( 89,237)( 90,238)( 91,240)( 92,239)( 93,234)( 94,233)( 95,235)( 96,236)
( 97,253)( 98,254)( 99,256)(100,255)(101,250)(102,249)(103,251)(104,252)
(105,245)(106,246)(107,248)(108,247)(109,242)(110,241)(111,243)(112,244)
(113,261)(114,262)(115,264)(116,263)(117,258)(118,257)(119,259)(120,260)
(121,277)(122,278)(123,280)(124,279)(125,274)(126,273)(127,275)(128,276)
(129,269)(130,270)(131,272)(132,271)(133,266)(134,265)(135,267)(136,268)
(137,285)(138,286)(139,288)(140,287)(141,282)(142,281)(143,283)(144,284);;
s2 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)
( 22, 24)( 25, 49)( 26, 50)( 27, 52)( 28, 51)( 29, 55)( 30, 56)( 31, 53)
( 32, 54)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)
( 40, 62)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)( 47, 69)
( 48, 70)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)( 91, 92)
( 93, 95)( 94, 96)( 97,121)( 98,122)( 99,124)(100,123)(101,127)(102,128)
(103,125)(104,126)(105,129)(106,130)(107,132)(108,131)(109,135)(110,136)
(111,133)(112,134)(113,137)(114,138)(115,140)(116,139)(117,143)(118,144)
(119,141)(120,142)(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)
(161,162)(165,168)(166,167)(169,194)(170,193)(171,195)(172,196)(173,200)
(174,199)(175,198)(176,197)(177,202)(178,201)(179,203)(180,204)(181,208)
(182,207)(183,206)(184,205)(185,210)(186,209)(187,211)(188,212)(189,216)
(190,215)(191,214)(192,213)(217,218)(221,224)(222,223)(225,226)(229,232)
(230,231)(233,234)(237,240)(238,239)(241,266)(242,265)(243,267)(244,268)
(245,272)(246,271)(247,270)(248,269)(249,274)(250,273)(251,275)(252,276)
(253,280)(254,279)(255,278)(256,277)(257,282)(258,281)(259,283)(260,284)
(261,288)(262,287)(263,286)(264,285);;
s3 := ( 1, 25)( 2, 26)( 3, 31)( 4, 32)( 5, 30)( 6, 29)( 7, 27)( 8, 28)
( 9, 33)( 10, 34)( 11, 39)( 12, 40)( 13, 38)( 14, 37)( 15, 35)( 16, 36)
( 17, 41)( 18, 42)( 19, 47)( 20, 48)( 21, 46)( 22, 45)( 23, 43)( 24, 44)
( 51, 55)( 52, 56)( 53, 54)( 59, 63)( 60, 64)( 61, 62)( 67, 71)( 68, 72)
( 69, 70)( 73, 97)( 74, 98)( 75,103)( 76,104)( 77,102)( 78,101)( 79, 99)
( 80,100)( 81,105)( 82,106)( 83,111)( 84,112)( 85,110)( 86,109)( 87,107)
( 88,108)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)( 94,117)( 95,115)
( 96,116)(123,127)(124,128)(125,126)(131,135)(132,136)(133,134)(139,143)
(140,144)(141,142)(145,170)(146,169)(147,176)(148,175)(149,173)(150,174)
(151,172)(152,171)(153,178)(154,177)(155,184)(156,183)(157,181)(158,182)
(159,180)(160,179)(161,186)(162,185)(163,192)(164,191)(165,189)(166,190)
(167,188)(168,187)(193,194)(195,200)(196,199)(201,202)(203,208)(204,207)
(209,210)(211,216)(212,215)(217,242)(218,241)(219,248)(220,247)(221,245)
(222,246)(223,244)(224,243)(225,250)(226,249)(227,256)(228,255)(229,253)
(230,254)(231,252)(232,251)(233,258)(234,257)(235,264)(236,263)(237,261)
(238,262)(239,260)(240,259)(265,266)(267,272)(268,271)(273,274)(275,280)
(276,279)(281,282)(283,288)(284,287);;
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, s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)
( 16, 24)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)
( 64, 72)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)
(112,120)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)
(152,224)(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)
(160,240)(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)
(168,232)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)
(176,248)(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)
(184,264)(185,249)(186,250)(187,251)(188,252)(189,253)(190,254)(191,255)
(192,256)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)
(200,272)(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)
(208,288)(209,273)(210,274)(211,275)(212,276)(213,277)(214,278)(215,279)
(216,280);
s1 := Sym(288)!( 1,157)( 2,158)( 3,160)( 4,159)( 5,154)( 6,153)( 7,155)
( 8,156)( 9,149)( 10,150)( 11,152)( 12,151)( 13,146)( 14,145)( 15,147)
( 16,148)( 17,165)( 18,166)( 19,168)( 20,167)( 21,162)( 22,161)( 23,163)
( 24,164)( 25,181)( 26,182)( 27,184)( 28,183)( 29,178)( 30,177)( 31,179)
( 32,180)( 33,173)( 34,174)( 35,176)( 36,175)( 37,170)( 38,169)( 39,171)
( 40,172)( 41,189)( 42,190)( 43,192)( 44,191)( 45,186)( 46,185)( 47,187)
( 48,188)( 49,205)( 50,206)( 51,208)( 52,207)( 53,202)( 54,201)( 55,203)
( 56,204)( 57,197)( 58,198)( 59,200)( 60,199)( 61,194)( 62,193)( 63,195)
( 64,196)( 65,213)( 66,214)( 67,216)( 68,215)( 69,210)( 70,209)( 71,211)
( 72,212)( 73,229)( 74,230)( 75,232)( 76,231)( 77,226)( 78,225)( 79,227)
( 80,228)( 81,221)( 82,222)( 83,224)( 84,223)( 85,218)( 86,217)( 87,219)
( 88,220)( 89,237)( 90,238)( 91,240)( 92,239)( 93,234)( 94,233)( 95,235)
( 96,236)( 97,253)( 98,254)( 99,256)(100,255)(101,250)(102,249)(103,251)
(104,252)(105,245)(106,246)(107,248)(108,247)(109,242)(110,241)(111,243)
(112,244)(113,261)(114,262)(115,264)(116,263)(117,258)(118,257)(119,259)
(120,260)(121,277)(122,278)(123,280)(124,279)(125,274)(126,273)(127,275)
(128,276)(129,269)(130,270)(131,272)(132,271)(133,266)(134,265)(135,267)
(136,268)(137,285)(138,286)(139,288)(140,287)(141,282)(142,281)(143,283)
(144,284);
s2 := Sym(288)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)
( 21, 23)( 22, 24)( 25, 49)( 26, 50)( 27, 52)( 28, 51)( 29, 55)( 30, 56)
( 31, 53)( 32, 54)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)
( 39, 61)( 40, 62)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)
( 47, 69)( 48, 70)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)
( 91, 92)( 93, 95)( 94, 96)( 97,121)( 98,122)( 99,124)(100,123)(101,127)
(102,128)(103,125)(104,126)(105,129)(106,130)(107,132)(108,131)(109,135)
(110,136)(111,133)(112,134)(113,137)(114,138)(115,140)(116,139)(117,143)
(118,144)(119,141)(120,142)(145,146)(149,152)(150,151)(153,154)(157,160)
(158,159)(161,162)(165,168)(166,167)(169,194)(170,193)(171,195)(172,196)
(173,200)(174,199)(175,198)(176,197)(177,202)(178,201)(179,203)(180,204)
(181,208)(182,207)(183,206)(184,205)(185,210)(186,209)(187,211)(188,212)
(189,216)(190,215)(191,214)(192,213)(217,218)(221,224)(222,223)(225,226)
(229,232)(230,231)(233,234)(237,240)(238,239)(241,266)(242,265)(243,267)
(244,268)(245,272)(246,271)(247,270)(248,269)(249,274)(250,273)(251,275)
(252,276)(253,280)(254,279)(255,278)(256,277)(257,282)(258,281)(259,283)
(260,284)(261,288)(262,287)(263,286)(264,285);
s3 := Sym(288)!( 1, 25)( 2, 26)( 3, 31)( 4, 32)( 5, 30)( 6, 29)( 7, 27)
( 8, 28)( 9, 33)( 10, 34)( 11, 39)( 12, 40)( 13, 38)( 14, 37)( 15, 35)
( 16, 36)( 17, 41)( 18, 42)( 19, 47)( 20, 48)( 21, 46)( 22, 45)( 23, 43)
( 24, 44)( 51, 55)( 52, 56)( 53, 54)( 59, 63)( 60, 64)( 61, 62)( 67, 71)
( 68, 72)( 69, 70)( 73, 97)( 74, 98)( 75,103)( 76,104)( 77,102)( 78,101)
( 79, 99)( 80,100)( 81,105)( 82,106)( 83,111)( 84,112)( 85,110)( 86,109)
( 87,107)( 88,108)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)( 94,117)
( 95,115)( 96,116)(123,127)(124,128)(125,126)(131,135)(132,136)(133,134)
(139,143)(140,144)(141,142)(145,170)(146,169)(147,176)(148,175)(149,173)
(150,174)(151,172)(152,171)(153,178)(154,177)(155,184)(156,183)(157,181)
(158,182)(159,180)(160,179)(161,186)(162,185)(163,192)(164,191)(165,189)
(166,190)(167,188)(168,187)(193,194)(195,200)(196,199)(201,202)(203,208)
(204,207)(209,210)(211,216)(212,215)(217,242)(218,241)(219,248)(220,247)
(221,245)(222,246)(223,244)(224,243)(225,250)(226,249)(227,256)(228,255)
(229,253)(230,254)(231,252)(232,251)(233,258)(234,257)(235,264)(236,263)
(237,261)(238,262)(239,260)(240,259)(265,266)(267,272)(268,271)(273,274)
(275,280)(276,279)(281,282)(283,288)(284,287);
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,
s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope