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