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