Polytope of Type {12,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,4}*1152d
if this polytope has a name.
Group : SmallGroup(1152,156063)
Rank : 4
Schlafli Type : {12,12,4}
Number of vertices, edges, etc : 12, 72, 24, 4
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {6,12,4}*576d, {12,6,4}*576d
3-fold quotients : {4,12,4}*384b
4-fold quotients : {6,6,4}*288d
6-fold quotients : {2,12,4}*192b, {4,6,4}*192b
12-fold quotients : {2,6,4}*96c
24-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)( 92, 96)(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)(116,120)(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)(140,144)(145,181)(146,182)(147,183)(148,184)(149,189)(150,190)(151,191)(152,192)(153,185)(154,186)(155,187)(156,188)(157,193)(158,194)(159,195)(160,196)(161,201)(162,202)(163,203)(164,204)(165,197)(166,198)(167,199)(168,200)(169,205)(170,206)(171,207)(172,208)(173,213)(174,214)(175,215)(176,216)(177,209)(178,210)(179,211)(180,212)(217,253)(218,254)(219,255)(220,256)(221,261)(222,262)(223,263)(224,264)(225,257)(226,258)(227,259)(228,260)(229,265)(230,266)(231,267)(232,268)(233,273)(234,274)(235,275)(236,276)(237,269)(238,270)(239,271)(240,272)(241,277)(242,278)(243,279)(244,280)(245,285)(246,286)(247,287)(248,288)(249,281)(250,282)(251,283)(252,284);;
s1 := ( 1,149)( 2,150)( 3,152)( 4,151)( 5,145)( 6,146)( 7,148)( 8,147)( 9,153)( 10,154)( 11,156)( 12,155)( 13,173)( 14,174)( 15,176)( 16,175)( 17,169)( 18,170)( 19,172)( 20,171)( 21,177)( 22,178)( 23,180)( 24,179)( 25,161)( 26,162)( 27,164)( 28,163)( 29,157)( 30,158)( 31,160)( 32,159)( 33,165)( 34,166)( 35,168)( 36,167)( 37,185)( 38,186)( 39,188)( 40,187)( 41,181)( 42,182)( 43,184)( 44,183)( 45,189)( 46,190)( 47,192)( 48,191)( 49,209)( 50,210)( 51,212)( 52,211)( 53,205)( 54,206)( 55,208)( 56,207)( 57,213)( 58,214)( 59,216)( 60,215)( 61,197)( 62,198)( 63,200)( 64,199)( 65,193)( 66,194)( 67,196)( 68,195)( 69,201)( 70,202)( 71,204)( 72,203)( 73,221)( 74,222)( 75,224)( 76,223)( 77,217)( 78,218)( 79,220)( 80,219)( 81,225)( 82,226)( 83,228)( 84,227)( 85,245)( 86,246)( 87,248)( 88,247)( 89,241)( 90,242)( 91,244)( 92,243)( 93,249)( 94,250)( 95,252)( 96,251)( 97,233)( 98,234)( 99,236)(100,235)(101,229)(102,230)(103,232)(104,231)(105,237)(106,238)(107,240)(108,239)(109,257)(110,258)(111,260)(112,259)(113,253)(114,254)(115,256)(116,255)(117,261)(118,262)(119,264)(120,263)(121,281)(122,282)(123,284)(124,283)(125,277)(126,278)(127,280)(128,279)(129,285)(130,286)(131,288)(132,287)(133,269)(134,270)(135,272)(136,271)(137,265)(138,266)(139,268)(140,267)(141,273)(142,274)(143,276)(144,275);;
s2 := ( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 17)( 6, 20)( 7, 19)( 8, 18)( 9, 21)( 10, 24)( 11, 23)( 12, 22)( 26, 28)( 30, 32)( 34, 36)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 53)( 42, 56)( 43, 55)( 44, 54)( 45, 57)( 46, 60)( 47, 59)( 48, 58)( 62, 64)( 66, 68)( 70, 72)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 93)( 82, 96)( 83, 95)( 84, 94)( 98,100)(102,104)(106,108)(109,121)(110,124)(111,123)(112,122)(113,125)(114,128)(115,127)(116,126)(117,129)(118,132)(119,131)(120,130)(134,136)(138,140)(142,144)(145,229)(146,232)(147,231)(148,230)(149,233)(150,236)(151,235)(152,234)(153,237)(154,240)(155,239)(156,238)(157,217)(158,220)(159,219)(160,218)(161,221)(162,224)(163,223)(164,222)(165,225)(166,228)(167,227)(168,226)(169,241)(170,244)(171,243)(172,242)(173,245)(174,248)(175,247)(176,246)(177,249)(178,252)(179,251)(180,250)(181,265)(182,268)(183,267)(184,266)(185,269)(186,272)(187,271)(188,270)(189,273)(190,276)(191,275)(192,274)(193,253)(194,256)(195,255)(196,254)(197,257)(198,260)(199,259)(200,258)(201,261)(202,264)(203,263)(204,262)(205,277)(206,280)(207,279)(208,278)(209,281)(210,284)(211,283)(212,282)(213,285)(214,288)(215,287)(216,286);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288);;
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*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*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,
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(288)!( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)( 92, 96)(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)(116,120)(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)(140,144)(145,181)(146,182)(147,183)(148,184)(149,189)(150,190)(151,191)(152,192)(153,185)(154,186)(155,187)(156,188)(157,193)(158,194)(159,195)(160,196)(161,201)(162,202)(163,203)(164,204)(165,197)(166,198)(167,199)(168,200)(169,205)(170,206)(171,207)(172,208)(173,213)(174,214)(175,215)(176,216)(177,209)(178,210)(179,211)(180,212)(217,253)(218,254)(219,255)(220,256)(221,261)(222,262)(223,263)(224,264)(225,257)(226,258)(227,259)(228,260)(229,265)(230,266)(231,267)(232,268)(233,273)(234,274)(235,275)(236,276)(237,269)(238,270)(239,271)(240,272)(241,277)(242,278)(243,279)(244,280)(245,285)(246,286)(247,287)(248,288)(249,281)(250,282)(251,283)(252,284);
s1 := Sym(288)!( 1,149)( 2,150)( 3,152)( 4,151)( 5,145)( 6,146)( 7,148)( 8,147)( 9,153)( 10,154)( 11,156)( 12,155)( 13,173)( 14,174)( 15,176)( 16,175)( 17,169)( 18,170)( 19,172)( 20,171)( 21,177)( 22,178)( 23,180)( 24,179)( 25,161)( 26,162)( 27,164)( 28,163)( 29,157)( 30,158)( 31,160)( 32,159)( 33,165)( 34,166)( 35,168)( 36,167)( 37,185)( 38,186)( 39,188)( 40,187)( 41,181)( 42,182)( 43,184)( 44,183)( 45,189)( 46,190)( 47,192)( 48,191)( 49,209)( 50,210)( 51,212)( 52,211)( 53,205)( 54,206)( 55,208)( 56,207)( 57,213)( 58,214)( 59,216)( 60,215)( 61,197)( 62,198)( 63,200)( 64,199)( 65,193)( 66,194)( 67,196)( 68,195)( 69,201)( 70,202)( 71,204)( 72,203)( 73,221)( 74,222)( 75,224)( 76,223)( 77,217)( 78,218)( 79,220)( 80,219)( 81,225)( 82,226)( 83,228)( 84,227)( 85,245)( 86,246)( 87,248)( 88,247)( 89,241)( 90,242)( 91,244)( 92,243)( 93,249)( 94,250)( 95,252)( 96,251)( 97,233)( 98,234)( 99,236)(100,235)(101,229)(102,230)(103,232)(104,231)(105,237)(106,238)(107,240)(108,239)(109,257)(110,258)(111,260)(112,259)(113,253)(114,254)(115,256)(116,255)(117,261)(118,262)(119,264)(120,263)(121,281)(122,282)(123,284)(124,283)(125,277)(126,278)(127,280)(128,279)(129,285)(130,286)(131,288)(132,287)(133,269)(134,270)(135,272)(136,271)(137,265)(138,266)(139,268)(140,267)(141,273)(142,274)(143,276)(144,275);
s2 := Sym(288)!( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 17)( 6, 20)( 7, 19)( 8, 18)( 9, 21)( 10, 24)( 11, 23)( 12, 22)( 26, 28)( 30, 32)( 34, 36)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 53)( 42, 56)( 43, 55)( 44, 54)( 45, 57)( 46, 60)( 47, 59)( 48, 58)( 62, 64)( 66, 68)( 70, 72)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 93)( 82, 96)( 83, 95)( 84, 94)( 98,100)(102,104)(106,108)(109,121)(110,124)(111,123)(112,122)(113,125)(114,128)(115,127)(116,126)(117,129)(118,132)(119,131)(120,130)(134,136)(138,140)(142,144)(145,229)(146,232)(147,231)(148,230)(149,233)(150,236)(151,235)(152,234)(153,237)(154,240)(155,239)(156,238)(157,217)(158,220)(159,219)(160,218)(161,221)(162,224)(163,223)(164,222)(165,225)(166,228)(167,227)(168,226)(169,241)(170,244)(171,243)(172,242)(173,245)(174,248)(175,247)(176,246)(177,249)(178,252)(179,251)(180,250)(181,265)(182,268)(183,267)(184,266)(185,269)(186,272)(187,271)(188,270)(189,273)(190,276)(191,275)(192,274)(193,253)(194,256)(195,255)(196,254)(197,257)(198,260)(199,259)(200,258)(201,261)(202,264)(203,263)(204,262)(205,277)(206,280)(207,279)(208,278)(209,281)(210,284)(211,283)(212,282)(213,285)(214,288)(215,287)(216,286);
s3 := Sym(288)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288);
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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*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,
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