Polytope of Type {4,6,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,12}*1152g
if this polytope has a name.
Group : SmallGroup(1152,157864)
Rank : 4
Schlafli Type : {4,6,12}
Number of vertices, edges, etc : 8, 24, 72, 12
Order of s0s1s2s3 : 6
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 : {4,6,12}*576f
3-fold quotients : {4,6,4}*384e
4-fold quotients : {2,6,12}*288d
6-fold quotients : {4,3,4}*192b, {4,6,4}*192e, {4,6,4}*192g
12-fold quotients : {2,6,4}*96b, {4,3,4}*96
24-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,153)( 2,154)( 3,155)( 4,156)( 5,157)( 6,158)( 7,159)( 8,160)
( 9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)( 16,152)
( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)( 24,176)
( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)( 32,168)
( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)( 40,192)
( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)( 48,184)
( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)( 56,208)
( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)( 64,200)
( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)( 72,224)
( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)( 80,216)
( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)( 88,240)
( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)( 96,232)
( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)(104,256)
(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)(112,248)
(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)(120,272)
(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)(128,264)
(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)(136,288)
(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)(144,280);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)( 23, 24)
( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 39, 40)( 41, 45)( 42, 46)
( 43, 48)( 44, 47)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)
( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)
( 63,108)( 64,107)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)
( 71,120)( 72,119)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)
( 79,124)( 80,123)( 81,129)( 82,130)( 83,132)( 84,131)( 85,133)( 86,134)
( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)( 94,138)
( 95,140)( 96,139)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)
(163,164)(167,168)(169,173)(170,174)(171,176)(172,175)(179,180)(183,184)
(185,189)(186,190)(187,192)(188,191)(193,241)(194,242)(195,244)(196,243)
(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)(204,255)
(205,249)(206,250)(207,252)(208,251)(209,257)(210,258)(211,260)(212,259)
(213,261)(214,262)(215,264)(216,263)(217,269)(218,270)(219,272)(220,271)
(221,265)(222,266)(223,268)(224,267)(225,273)(226,274)(227,276)(228,275)
(229,277)(230,278)(231,280)(232,279)(233,285)(234,286)(235,288)(236,287)
(237,281)(238,282)(239,284)(240,283);;
s2 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 61)( 6, 64)( 7, 63)( 8, 62)
( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 53)( 14, 56)( 15, 55)( 16, 54)
( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 93)( 22, 96)( 23, 95)( 24, 94)
( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)
( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 77)( 38, 80)( 39, 79)( 40, 78)
( 41, 73)( 42, 76)( 43, 75)( 44, 74)( 45, 69)( 46, 72)( 47, 71)( 48, 70)
( 98,100)(101,109)(102,112)(103,111)(104,110)(106,108)(113,129)(114,132)
(115,131)(116,130)(117,141)(118,144)(119,143)(120,142)(121,137)(122,140)
(123,139)(124,138)(125,133)(126,136)(127,135)(128,134)(145,193)(146,196)
(147,195)(148,194)(149,205)(150,208)(151,207)(152,206)(153,201)(154,204)
(155,203)(156,202)(157,197)(158,200)(159,199)(160,198)(161,225)(162,228)
(163,227)(164,226)(165,237)(166,240)(167,239)(168,238)(169,233)(170,236)
(171,235)(172,234)(173,229)(174,232)(175,231)(176,230)(177,209)(178,212)
(179,211)(180,210)(181,221)(182,224)(183,223)(184,222)(185,217)(186,220)
(187,219)(188,218)(189,213)(190,216)(191,215)(192,214)(242,244)(245,253)
(246,256)(247,255)(248,254)(250,252)(257,273)(258,276)(259,275)(260,274)
(261,285)(262,288)(263,287)(264,286)(265,281)(266,284)(267,283)(268,282)
(269,277)(270,280)(271,279)(272,278);;
s3 := ( 1, 18)( 2, 17)( 3, 20)( 4, 19)( 5, 22)( 6, 21)( 7, 24)( 8, 23)
( 9, 26)( 10, 25)( 11, 28)( 12, 27)( 13, 30)( 14, 29)( 15, 32)( 16, 31)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 66)( 50, 65)( 51, 68)( 52, 67)( 53, 70)( 54, 69)( 55, 72)( 56, 71)
( 57, 74)( 58, 73)( 59, 76)( 60, 75)( 61, 78)( 62, 77)( 63, 80)( 64, 79)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97,114)( 98,113)( 99,116)(100,115)(101,118)(102,117)(103,120)(104,119)
(105,122)(106,121)(107,124)(108,123)(109,126)(110,125)(111,128)(112,127)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,162)(146,161)(147,164)(148,163)(149,166)(150,165)(151,168)(152,167)
(153,170)(154,169)(155,172)(156,171)(157,174)(158,173)(159,176)(160,175)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,210)(194,209)(195,212)(196,211)(197,214)(198,213)(199,216)(200,215)
(201,218)(202,217)(203,220)(204,219)(205,222)(206,221)(207,224)(208,223)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,258)(242,257)(243,260)(244,259)(245,262)(246,261)(247,264)(248,263)
(249,266)(250,265)(251,268)(252,267)(253,270)(254,269)(255,272)(256,271)
(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*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s1*s2*s3*s1*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1,153)( 2,154)( 3,155)( 4,156)( 5,157)( 6,158)( 7,159)
( 8,160)( 9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)
( 16,152)( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)
( 24,176)( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)
( 32,168)( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)
( 40,192)( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)
( 48,184)( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)
( 56,208)( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)
( 64,200)( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)
( 72,224)( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)
( 80,216)( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)
( 88,240)( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)
( 96,232)( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)
(104,256)(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)
(112,248)(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)
(120,272)(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)
(128,264)(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)
(136,288)(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)
(144,280);
s1 := Sym(288)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)
( 23, 24)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 39, 40)( 41, 45)
( 42, 46)( 43, 48)( 44, 47)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)
( 54,102)( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)
( 62,106)( 63,108)( 64,107)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)
( 70,118)( 71,120)( 72,119)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)
( 78,122)( 79,124)( 80,123)( 81,129)( 82,130)( 83,132)( 84,131)( 85,133)
( 86,134)( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)
( 94,138)( 95,140)( 96,139)(147,148)(151,152)(153,157)(154,158)(155,160)
(156,159)(163,164)(167,168)(169,173)(170,174)(171,176)(172,175)(179,180)
(183,184)(185,189)(186,190)(187,192)(188,191)(193,241)(194,242)(195,244)
(196,243)(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)
(204,255)(205,249)(206,250)(207,252)(208,251)(209,257)(210,258)(211,260)
(212,259)(213,261)(214,262)(215,264)(216,263)(217,269)(218,270)(219,272)
(220,271)(221,265)(222,266)(223,268)(224,267)(225,273)(226,274)(227,276)
(228,275)(229,277)(230,278)(231,280)(232,279)(233,285)(234,286)(235,288)
(236,287)(237,281)(238,282)(239,284)(240,283);
s2 := Sym(288)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 61)( 6, 64)( 7, 63)
( 8, 62)( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 53)( 14, 56)( 15, 55)
( 16, 54)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 93)( 22, 96)( 23, 95)
( 24, 94)( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)
( 32, 86)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 77)( 38, 80)( 39, 79)
( 40, 78)( 41, 73)( 42, 76)( 43, 75)( 44, 74)( 45, 69)( 46, 72)( 47, 71)
( 48, 70)( 98,100)(101,109)(102,112)(103,111)(104,110)(106,108)(113,129)
(114,132)(115,131)(116,130)(117,141)(118,144)(119,143)(120,142)(121,137)
(122,140)(123,139)(124,138)(125,133)(126,136)(127,135)(128,134)(145,193)
(146,196)(147,195)(148,194)(149,205)(150,208)(151,207)(152,206)(153,201)
(154,204)(155,203)(156,202)(157,197)(158,200)(159,199)(160,198)(161,225)
(162,228)(163,227)(164,226)(165,237)(166,240)(167,239)(168,238)(169,233)
(170,236)(171,235)(172,234)(173,229)(174,232)(175,231)(176,230)(177,209)
(178,212)(179,211)(180,210)(181,221)(182,224)(183,223)(184,222)(185,217)
(186,220)(187,219)(188,218)(189,213)(190,216)(191,215)(192,214)(242,244)
(245,253)(246,256)(247,255)(248,254)(250,252)(257,273)(258,276)(259,275)
(260,274)(261,285)(262,288)(263,287)(264,286)(265,281)(266,284)(267,283)
(268,282)(269,277)(270,280)(271,279)(272,278);
s3 := Sym(288)!( 1, 18)( 2, 17)( 3, 20)( 4, 19)( 5, 22)( 6, 21)( 7, 24)
( 8, 23)( 9, 26)( 10, 25)( 11, 28)( 12, 27)( 13, 30)( 14, 29)( 15, 32)
( 16, 31)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 66)( 50, 65)( 51, 68)( 52, 67)( 53, 70)( 54, 69)( 55, 72)
( 56, 71)( 57, 74)( 58, 73)( 59, 76)( 60, 75)( 61, 78)( 62, 77)( 63, 80)
( 64, 79)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97,114)( 98,113)( 99,116)(100,115)(101,118)(102,117)(103,120)
(104,119)(105,122)(106,121)(107,124)(108,123)(109,126)(110,125)(111,128)
(112,127)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,162)(146,161)(147,164)(148,163)(149,166)(150,165)(151,168)
(152,167)(153,170)(154,169)(155,172)(156,171)(157,174)(158,173)(159,176)
(160,175)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,210)(194,209)(195,212)(196,211)(197,214)(198,213)(199,216)
(200,215)(201,218)(202,217)(203,220)(204,219)(205,222)(206,221)(207,224)
(208,223)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,258)(242,257)(243,260)(244,259)(245,262)(246,261)(247,264)
(248,263)(249,266)(250,265)(251,268)(252,267)(253,270)(254,269)(255,272)
(256,271)(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*s0*s1*s0*s1*s0*s1, s1*s2*s3*s1*s2*s3*s1*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;
References : None.
to this polytope