Polytope of Type {4,3,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157864)
Rank : 4
Schlafli Type : {4,3,12}
Number of vertices, edges, etc : 8, 24, 72, 24
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {4,3,12}*576
3-fold quotients : {4,3,4}*384
4-fold quotients : {4,3,6}*288, {2,3,12}*288
6-fold quotients : {4,3,4}*192a, {4,3,4}*192b
8-fold quotients : {4,3,6}*144
12-fold quotients : {2,3,4}*96, {4,3,2}*96, {4,3,4}*96
16-fold quotients : {2,3,6}*72
24-fold quotients : {2,3,4}*48, {4,3,2}*48
48-fold quotients : {2,3,2}*24
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)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 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)( 65,129)( 66,130)
( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)( 73,141)( 74,142)
( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,113)( 82,114)
( 83,116)( 84,115)( 85,117)( 86,118)( 87,120)( 88,119)( 89,125)( 90,126)
( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)(147,148)(151,152)
(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)
(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)
(173,185)(174,186)(175,188)(176,187)(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)(209,273)(210,274)(211,276)(212,275)
(213,277)(214,278)(215,280)(216,279)(217,285)(218,286)(219,288)(220,287)
(221,281)(222,282)(223,284)(224,283)(225,257)(226,258)(227,260)(228,259)
(229,261)(230,262)(231,264)(232,263)(233,269)(234,270)(235,272)(236,271)
(237,265)(238,266)(239,268)(240,267);;
s2 := ( 1, 65)( 2, 68)( 3, 67)( 4, 66)( 5, 77)( 6, 80)( 7, 79)( 8, 78)
( 9, 73)( 10, 76)( 11, 75)( 12, 74)( 13, 69)( 14, 72)( 15, 71)( 16, 70)
( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 61)( 22, 64)( 23, 63)( 24, 62)
( 25, 57)( 26, 60)( 27, 59)( 28, 58)( 29, 53)( 30, 56)( 31, 55)( 32, 54)
( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37, 93)( 38, 96)( 39, 95)( 40, 94)
( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 85)( 46, 88)( 47, 87)( 48, 86)
( 97,113)( 98,116)( 99,115)(100,114)(101,125)(102,128)(103,127)(104,126)
(105,121)(106,124)(107,123)(108,122)(109,117)(110,120)(111,119)(112,118)
(130,132)(133,141)(134,144)(135,143)(136,142)(138,140)(145,209)(146,212)
(147,211)(148,210)(149,221)(150,224)(151,223)(152,222)(153,217)(154,220)
(155,219)(156,218)(157,213)(158,216)(159,215)(160,214)(161,193)(162,196)
(163,195)(164,194)(165,205)(166,208)(167,207)(168,206)(169,201)(170,204)
(171,203)(172,202)(173,197)(174,200)(175,199)(176,198)(177,225)(178,228)
(179,227)(180,226)(181,237)(182,240)(183,239)(184,238)(185,233)(186,236)
(187,235)(188,234)(189,229)(190,232)(191,231)(192,230)(241,257)(242,260)
(243,259)(244,258)(245,269)(246,272)(247,271)(248,270)(249,265)(250,268)
(251,267)(252,266)(253,261)(254,264)(255,263)(256,262)(274,276)(277,285)
(278,288)(279,287)(280,286)(282,284);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 34)( 18, 33)( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 40)( 24, 39)
( 25, 42)( 26, 41)( 27, 44)( 28, 43)( 29, 46)( 30, 45)( 31, 48)( 32, 47)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 82)( 66, 81)( 67, 84)( 68, 83)( 69, 86)( 70, 85)( 71, 88)( 72, 87)
( 73, 90)( 74, 89)( 75, 92)( 76, 91)( 77, 94)( 78, 93)( 79, 96)( 80, 95)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,130)(114,129)(115,132)(116,131)(117,134)(118,133)(119,136)(120,135)
(121,138)(122,137)(123,140)(124,139)(125,142)(126,141)(127,144)(128,143)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,178)(162,177)(163,180)(164,179)(165,182)(166,181)(167,184)(168,183)
(169,186)(170,185)(171,188)(172,187)(173,190)(174,189)(175,192)(176,191)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,226)(210,225)(211,228)(212,227)(213,230)(214,229)(215,232)(216,231)
(217,234)(218,233)(219,236)(220,235)(221,238)(222,237)(223,240)(224,239)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,274)(258,273)(259,276)(260,275)(261,278)(262,277)(263,280)(264,279)
(265,282)(266,281)(267,284)(268,283)(269,286)(270,285)(271,288)(272,287);;
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, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*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)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)
( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 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)( 65,129)
( 66,130)( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)( 73,141)
( 74,142)( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,113)
( 82,114)( 83,116)( 84,115)( 85,117)( 86,118)( 87,120)( 88,119)( 89,125)
( 90,126)( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)(147,148)
(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)
(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)
(172,191)(173,185)(174,186)(175,188)(176,187)(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)(209,273)(210,274)(211,276)
(212,275)(213,277)(214,278)(215,280)(216,279)(217,285)(218,286)(219,288)
(220,287)(221,281)(222,282)(223,284)(224,283)(225,257)(226,258)(227,260)
(228,259)(229,261)(230,262)(231,264)(232,263)(233,269)(234,270)(235,272)
(236,271)(237,265)(238,266)(239,268)(240,267);
s2 := Sym(288)!( 1, 65)( 2, 68)( 3, 67)( 4, 66)( 5, 77)( 6, 80)( 7, 79)
( 8, 78)( 9, 73)( 10, 76)( 11, 75)( 12, 74)( 13, 69)( 14, 72)( 15, 71)
( 16, 70)( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 61)( 22, 64)( 23, 63)
( 24, 62)( 25, 57)( 26, 60)( 27, 59)( 28, 58)( 29, 53)( 30, 56)( 31, 55)
( 32, 54)( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37, 93)( 38, 96)( 39, 95)
( 40, 94)( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 85)( 46, 88)( 47, 87)
( 48, 86)( 97,113)( 98,116)( 99,115)(100,114)(101,125)(102,128)(103,127)
(104,126)(105,121)(106,124)(107,123)(108,122)(109,117)(110,120)(111,119)
(112,118)(130,132)(133,141)(134,144)(135,143)(136,142)(138,140)(145,209)
(146,212)(147,211)(148,210)(149,221)(150,224)(151,223)(152,222)(153,217)
(154,220)(155,219)(156,218)(157,213)(158,216)(159,215)(160,214)(161,193)
(162,196)(163,195)(164,194)(165,205)(166,208)(167,207)(168,206)(169,201)
(170,204)(171,203)(172,202)(173,197)(174,200)(175,199)(176,198)(177,225)
(178,228)(179,227)(180,226)(181,237)(182,240)(183,239)(184,238)(185,233)
(186,236)(187,235)(188,234)(189,229)(190,232)(191,231)(192,230)(241,257)
(242,260)(243,259)(244,258)(245,269)(246,272)(247,271)(248,270)(249,265)
(250,268)(251,267)(252,266)(253,261)(254,264)(255,263)(256,262)(274,276)
(277,285)(278,288)(279,287)(280,286)(282,284);
s3 := Sym(288)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 34)( 18, 33)( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 40)
( 24, 39)( 25, 42)( 26, 41)( 27, 44)( 28, 43)( 29, 46)( 30, 45)( 31, 48)
( 32, 47)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 82)( 66, 81)( 67, 84)( 68, 83)( 69, 86)( 70, 85)( 71, 88)
( 72, 87)( 73, 90)( 74, 89)( 75, 92)( 76, 91)( 77, 94)( 78, 93)( 79, 96)
( 80, 95)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,130)(114,129)(115,132)(116,131)(117,134)(118,133)(119,136)
(120,135)(121,138)(122,137)(123,140)(124,139)(125,142)(126,141)(127,144)
(128,143)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,178)(162,177)(163,180)(164,179)(165,182)(166,181)(167,184)
(168,183)(169,186)(170,185)(171,188)(172,187)(173,190)(174,189)(175,192)
(176,191)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,226)(210,225)(211,228)(212,227)(213,230)(214,229)(215,232)
(216,231)(217,234)(218,233)(219,236)(220,235)(221,238)(222,237)(223,240)
(224,239)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,274)(258,273)(259,276)(260,275)(261,278)(262,277)(263,280)
(264,279)(265,282)(266,281)(267,284)(268,283)(269,286)(270,285)(271,288)
(272,287);
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,
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >;
References : None.
to this polytope