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