Polytope of Type {6,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,6}*1152c
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 4
Schlafli Type : {6,12,6}
Number of vertices, edges, etc : 6, 48, 48, 8
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {6,12,3}*576, {6,6,6}*576a
3-fold quotients : {2,12,6}*384b
4-fold quotients : {6,6,3}*288
6-fold quotients : {2,12,3}*192, {2,6,6}*192
12-fold quotients : {2,3,6}*96, {2,6,3}*96
24-fold quotients : {2,3,3}*48, {6,2,2}*48
48-fold quotients : {3,2,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)(160,168)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(249,257)(250,258)(251,259)(252,260)(253,261)(254,262)(255,263)(256,264)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288);;
s1 := ( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)( 8, 14)
( 19, 20)( 21, 23)( 22, 24)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 63)
( 30, 64)( 31, 61)( 32, 62)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 55)
( 38, 56)( 39, 53)( 40, 54)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)
( 46, 72)( 47, 69)( 48, 70)( 73, 82)( 74, 81)( 75, 83)( 76, 84)( 77, 88)
( 78, 87)( 79, 86)( 80, 85)( 89, 90)( 93, 96)( 94, 95)( 97,130)( 98,129)
( 99,131)(100,132)(101,136)(102,135)(103,134)(104,133)(105,122)(106,121)
(107,123)(108,124)(109,128)(110,127)(111,126)(112,125)(113,138)(114,137)
(115,139)(116,140)(117,144)(118,143)(119,142)(120,141)(145,153)(146,154)
(147,156)(148,155)(149,159)(150,160)(151,157)(152,158)(163,164)(165,167)
(166,168)(169,201)(170,202)(171,204)(172,203)(173,207)(174,208)(175,205)
(176,206)(177,193)(178,194)(179,196)(180,195)(181,199)(182,200)(183,197)
(184,198)(185,209)(186,210)(187,212)(188,211)(189,215)(190,216)(191,213)
(192,214)(217,226)(218,225)(219,227)(220,228)(221,232)(222,231)(223,230)
(224,229)(233,234)(237,240)(238,239)(241,274)(242,273)(243,275)(244,276)
(245,280)(246,279)(247,278)(248,277)(249,266)(250,265)(251,267)(252,268)
(253,272)(254,271)(255,270)(256,269)(257,282)(258,281)(259,283)(260,284)
(261,288)(262,287)(263,286)(264,285);;
s2 := ( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,102)( 6,101)( 7, 99)( 8,100)
( 9,105)( 10,106)( 11,111)( 12,112)( 13,110)( 14,109)( 15,107)( 16,108)
( 17,113)( 18,114)( 19,119)( 20,120)( 21,118)( 22,117)( 23,115)( 24,116)
( 25, 73)( 26, 74)( 27, 79)( 28, 80)( 29, 78)( 30, 77)( 31, 75)( 32, 76)
( 33, 81)( 34, 82)( 35, 87)( 36, 88)( 37, 86)( 38, 85)( 39, 83)( 40, 84)
( 41, 89)( 42, 90)( 43, 95)( 44, 96)( 45, 94)( 46, 93)( 47, 91)( 48, 92)
( 49,121)( 50,122)( 51,127)( 52,128)( 53,126)( 54,125)( 55,123)( 56,124)
( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)( 64,132)
( 65,137)( 66,138)( 67,143)( 68,144)( 69,142)( 70,141)( 71,139)( 72,140)
(145,241)(146,242)(147,247)(148,248)(149,246)(150,245)(151,243)(152,244)
(153,249)(154,250)(155,255)(156,256)(157,254)(158,253)(159,251)(160,252)
(161,257)(162,258)(163,263)(164,264)(165,262)(166,261)(167,259)(168,260)
(169,217)(170,218)(171,223)(172,224)(173,222)(174,221)(175,219)(176,220)
(177,225)(178,226)(179,231)(180,232)(181,230)(182,229)(183,227)(184,228)
(185,233)(186,234)(187,239)(188,240)(189,238)(190,237)(191,235)(192,236)
(193,265)(194,266)(195,271)(196,272)(197,270)(198,269)(199,267)(200,268)
(201,273)(202,274)(203,279)(204,280)(205,278)(206,277)(207,275)(208,276)
(209,281)(210,282)(211,287)(212,288)(213,286)(214,285)(215,283)(216,284);;
s3 := ( 1,219)( 2,220)( 3,217)( 4,218)( 5,222)( 6,221)( 7,223)( 8,224)
( 9,227)( 10,228)( 11,225)( 12,226)( 13,230)( 14,229)( 15,231)( 16,232)
( 17,235)( 18,236)( 19,233)( 20,234)( 21,238)( 22,237)( 23,239)( 24,240)
( 25,267)( 26,268)( 27,265)( 28,266)( 29,270)( 30,269)( 31,271)( 32,272)
( 33,275)( 34,276)( 35,273)( 36,274)( 37,278)( 38,277)( 39,279)( 40,280)
( 41,283)( 42,284)( 43,281)( 44,282)( 45,286)( 46,285)( 47,287)( 48,288)
( 49,243)( 50,244)( 51,241)( 52,242)( 53,246)( 54,245)( 55,247)( 56,248)
( 57,251)( 58,252)( 59,249)( 60,250)( 61,254)( 62,253)( 63,255)( 64,256)
( 65,259)( 66,260)( 67,257)( 68,258)( 69,262)( 70,261)( 71,263)( 72,264)
( 73,147)( 74,148)( 75,145)( 76,146)( 77,150)( 78,149)( 79,151)( 80,152)
( 81,155)( 82,156)( 83,153)( 84,154)( 85,158)( 86,157)( 87,159)( 88,160)
( 89,163)( 90,164)( 91,161)( 92,162)( 93,166)( 94,165)( 95,167)( 96,168)
( 97,195)( 98,196)( 99,193)(100,194)(101,198)(102,197)(103,199)(104,200)
(105,203)(106,204)(107,201)(108,202)(109,206)(110,205)(111,207)(112,208)
(113,211)(114,212)(115,209)(116,210)(117,214)(118,213)(119,215)(120,216)
(121,171)(122,172)(123,169)(124,170)(125,174)(126,173)(127,175)(128,176)
(129,179)(130,180)(131,177)(132,178)(133,182)(134,181)(135,183)(136,184)
(137,187)(138,188)(139,185)(140,186)(141,190)(142,189)(143,191)(144,192);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)
( 16, 24)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)
( 64, 72)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)
(112,120)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)
(160,168)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)
(208,216)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(249,257)(250,258)(251,259)(252,260)(253,261)(254,262)(255,263)
(256,264)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288);
s1 := Sym(288)!( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)
( 8, 14)( 19, 20)( 21, 23)( 22, 24)( 25, 57)( 26, 58)( 27, 60)( 28, 59)
( 29, 63)( 30, 64)( 31, 61)( 32, 62)( 33, 49)( 34, 50)( 35, 52)( 36, 51)
( 37, 55)( 38, 56)( 39, 53)( 40, 54)( 41, 65)( 42, 66)( 43, 68)( 44, 67)
( 45, 71)( 46, 72)( 47, 69)( 48, 70)( 73, 82)( 74, 81)( 75, 83)( 76, 84)
( 77, 88)( 78, 87)( 79, 86)( 80, 85)( 89, 90)( 93, 96)( 94, 95)( 97,130)
( 98,129)( 99,131)(100,132)(101,136)(102,135)(103,134)(104,133)(105,122)
(106,121)(107,123)(108,124)(109,128)(110,127)(111,126)(112,125)(113,138)
(114,137)(115,139)(116,140)(117,144)(118,143)(119,142)(120,141)(145,153)
(146,154)(147,156)(148,155)(149,159)(150,160)(151,157)(152,158)(163,164)
(165,167)(166,168)(169,201)(170,202)(171,204)(172,203)(173,207)(174,208)
(175,205)(176,206)(177,193)(178,194)(179,196)(180,195)(181,199)(182,200)
(183,197)(184,198)(185,209)(186,210)(187,212)(188,211)(189,215)(190,216)
(191,213)(192,214)(217,226)(218,225)(219,227)(220,228)(221,232)(222,231)
(223,230)(224,229)(233,234)(237,240)(238,239)(241,274)(242,273)(243,275)
(244,276)(245,280)(246,279)(247,278)(248,277)(249,266)(250,265)(251,267)
(252,268)(253,272)(254,271)(255,270)(256,269)(257,282)(258,281)(259,283)
(260,284)(261,288)(262,287)(263,286)(264,285);
s2 := Sym(288)!( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,102)( 6,101)( 7, 99)
( 8,100)( 9,105)( 10,106)( 11,111)( 12,112)( 13,110)( 14,109)( 15,107)
( 16,108)( 17,113)( 18,114)( 19,119)( 20,120)( 21,118)( 22,117)( 23,115)
( 24,116)( 25, 73)( 26, 74)( 27, 79)( 28, 80)( 29, 78)( 30, 77)( 31, 75)
( 32, 76)( 33, 81)( 34, 82)( 35, 87)( 36, 88)( 37, 86)( 38, 85)( 39, 83)
( 40, 84)( 41, 89)( 42, 90)( 43, 95)( 44, 96)( 45, 94)( 46, 93)( 47, 91)
( 48, 92)( 49,121)( 50,122)( 51,127)( 52,128)( 53,126)( 54,125)( 55,123)
( 56,124)( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)
( 64,132)( 65,137)( 66,138)( 67,143)( 68,144)( 69,142)( 70,141)( 71,139)
( 72,140)(145,241)(146,242)(147,247)(148,248)(149,246)(150,245)(151,243)
(152,244)(153,249)(154,250)(155,255)(156,256)(157,254)(158,253)(159,251)
(160,252)(161,257)(162,258)(163,263)(164,264)(165,262)(166,261)(167,259)
(168,260)(169,217)(170,218)(171,223)(172,224)(173,222)(174,221)(175,219)
(176,220)(177,225)(178,226)(179,231)(180,232)(181,230)(182,229)(183,227)
(184,228)(185,233)(186,234)(187,239)(188,240)(189,238)(190,237)(191,235)
(192,236)(193,265)(194,266)(195,271)(196,272)(197,270)(198,269)(199,267)
(200,268)(201,273)(202,274)(203,279)(204,280)(205,278)(206,277)(207,275)
(208,276)(209,281)(210,282)(211,287)(212,288)(213,286)(214,285)(215,283)
(216,284);
s3 := Sym(288)!( 1,219)( 2,220)( 3,217)( 4,218)( 5,222)( 6,221)( 7,223)
( 8,224)( 9,227)( 10,228)( 11,225)( 12,226)( 13,230)( 14,229)( 15,231)
( 16,232)( 17,235)( 18,236)( 19,233)( 20,234)( 21,238)( 22,237)( 23,239)
( 24,240)( 25,267)( 26,268)( 27,265)( 28,266)( 29,270)( 30,269)( 31,271)
( 32,272)( 33,275)( 34,276)( 35,273)( 36,274)( 37,278)( 38,277)( 39,279)
( 40,280)( 41,283)( 42,284)( 43,281)( 44,282)( 45,286)( 46,285)( 47,287)
( 48,288)( 49,243)( 50,244)( 51,241)( 52,242)( 53,246)( 54,245)( 55,247)
( 56,248)( 57,251)( 58,252)( 59,249)( 60,250)( 61,254)( 62,253)( 63,255)
( 64,256)( 65,259)( 66,260)( 67,257)( 68,258)( 69,262)( 70,261)( 71,263)
( 72,264)( 73,147)( 74,148)( 75,145)( 76,146)( 77,150)( 78,149)( 79,151)
( 80,152)( 81,155)( 82,156)( 83,153)( 84,154)( 85,158)( 86,157)( 87,159)
( 88,160)( 89,163)( 90,164)( 91,161)( 92,162)( 93,166)( 94,165)( 95,167)
( 96,168)( 97,195)( 98,196)( 99,193)(100,194)(101,198)(102,197)(103,199)
(104,200)(105,203)(106,204)(107,201)(108,202)(109,206)(110,205)(111,207)
(112,208)(113,211)(114,212)(115,209)(116,210)(117,214)(118,213)(119,215)
(120,216)(121,171)(122,172)(123,169)(124,170)(125,174)(126,173)(127,175)
(128,176)(129,179)(130,180)(131,177)(132,178)(133,182)(134,181)(135,183)
(136,184)(137,187)(138,188)(139,185)(140,186)(141,190)(142,189)(143,191)
(144,192);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope