Polytope of Type {12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*1152j
if this polytope has a name.
Group : SmallGroup(1152,157851)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 96, 288, 48
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,3}*576
4-fold quotients : {6,6}*288a, {12,6}*288b
8-fold quotients : {6,3}*144, {12,3}*144
12-fold quotients : {4,6}*96, {6,6}*96
16-fold quotients : {6,6}*72b
24-fold quotients : {3,6}*48, {4,3}*48, {4,6}*48b, {4,6}*48c, {6,3}*48
32-fold quotients : {6,3}*36
48-fold quotients : {3,3}*24, {4,3}*24, {2,6}*24
96-fold quotients : {2,3}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 13)( 6, 14)( 7, 16)( 8, 15)
( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 29)( 22, 30)( 23, 32)( 24, 31)
( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)( 40, 47)
( 49,105)( 50,106)( 51,108)( 52,107)( 53,109)( 54,110)( 55,112)( 56,111)
( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,101)( 62,102)( 63,104)( 64,103)
( 65,121)( 66,122)( 67,124)( 68,123)( 69,125)( 70,126)( 71,128)( 72,127)
( 73,113)( 74,114)( 75,116)( 76,115)( 77,117)( 78,118)( 79,120)( 80,119)
( 81,137)( 82,138)( 83,140)( 84,139)( 85,141)( 86,142)( 87,144)( 88,143)
( 89,129)( 90,130)( 91,132)( 92,131)( 93,133)( 94,134)( 95,136)( 96,135)
(145,153)(146,154)(147,156)(148,155)(149,157)(150,158)(151,160)(152,159)
(161,169)(162,170)(163,172)(164,171)(165,173)(166,174)(167,176)(168,175)
(177,185)(178,186)(179,188)(180,187)(181,189)(182,190)(183,192)(184,191)
(193,249)(194,250)(195,252)(196,251)(197,253)(198,254)(199,256)(200,255)
(201,241)(202,242)(203,244)(204,243)(205,245)(206,246)(207,248)(208,247)
(209,265)(210,266)(211,268)(212,267)(213,269)(214,270)(215,272)(216,271)
(217,257)(218,258)(219,260)(220,259)(221,261)(222,262)(223,264)(224,263)
(225,281)(226,282)(227,284)(228,283)(229,285)(230,286)(231,288)(232,287)
(233,273)(234,274)(235,276)(236,275)(237,277)(238,278)(239,280)(240,279);;
s1 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 53)( 6, 56)( 7, 55)( 8, 54)
( 9, 61)( 10, 64)( 11, 63)( 12, 62)( 13, 57)( 14, 60)( 15, 59)( 16, 58)
( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 85)( 22, 88)( 23, 87)( 24, 86)
( 25, 93)( 26, 96)( 27, 95)( 28, 94)( 29, 89)( 30, 92)( 31, 91)( 32, 90)
( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 69)( 38, 72)( 39, 71)( 40, 70)
( 41, 77)( 42, 80)( 43, 79)( 44, 78)( 45, 73)( 46, 76)( 47, 75)( 48, 74)
( 98,100)(102,104)(105,109)(106,112)(107,111)(108,110)(113,129)(114,132)
(115,131)(116,130)(117,133)(118,136)(119,135)(120,134)(121,141)(122,144)
(123,143)(124,142)(125,137)(126,140)(127,139)(128,138)(145,193)(146,196)
(147,195)(148,194)(149,197)(150,200)(151,199)(152,198)(153,205)(154,208)
(155,207)(156,206)(157,201)(158,204)(159,203)(160,202)(161,225)(162,228)
(163,227)(164,226)(165,229)(166,232)(167,231)(168,230)(169,237)(170,240)
(171,239)(172,238)(173,233)(174,236)(175,235)(176,234)(177,209)(178,212)
(179,211)(180,210)(181,213)(182,216)(183,215)(184,214)(185,221)(186,224)
(187,223)(188,222)(189,217)(190,220)(191,219)(192,218)(242,244)(246,248)
(249,253)(250,256)(251,255)(252,254)(257,273)(258,276)(259,275)(260,274)
(261,277)(262,280)(263,279)(264,278)(265,285)(266,288)(267,287)(268,286)
(269,281)(270,284)(271,283)(272,282);;
s2 := ( 1,162)( 2,161)( 3,163)( 4,164)( 5,174)( 6,173)( 7,175)( 8,176)
( 9,170)( 10,169)( 11,171)( 12,172)( 13,166)( 14,165)( 15,167)( 16,168)
( 17,146)( 18,145)( 19,147)( 20,148)( 21,158)( 22,157)( 23,159)( 24,160)
( 25,154)( 26,153)( 27,155)( 28,156)( 29,150)( 30,149)( 31,151)( 32,152)
( 33,178)( 34,177)( 35,179)( 36,180)( 37,190)( 38,189)( 39,191)( 40,192)
( 41,186)( 42,185)( 43,187)( 44,188)( 45,182)( 46,181)( 47,183)( 48,184)
( 49,258)( 50,257)( 51,259)( 52,260)( 53,270)( 54,269)( 55,271)( 56,272)
( 57,266)( 58,265)( 59,267)( 60,268)( 61,262)( 62,261)( 63,263)( 64,264)
( 65,242)( 66,241)( 67,243)( 68,244)( 69,254)( 70,253)( 71,255)( 72,256)
( 73,250)( 74,249)( 75,251)( 76,252)( 77,246)( 78,245)( 79,247)( 80,248)
( 81,274)( 82,273)( 83,275)( 84,276)( 85,286)( 86,285)( 87,287)( 88,288)
( 89,282)( 90,281)( 91,283)( 92,284)( 93,278)( 94,277)( 95,279)( 96,280)
( 97,210)( 98,209)( 99,211)(100,212)(101,222)(102,221)(103,223)(104,224)
(105,218)(106,217)(107,219)(108,220)(109,214)(110,213)(111,215)(112,216)
(113,194)(114,193)(115,195)(116,196)(117,206)(118,205)(119,207)(120,208)
(121,202)(122,201)(123,203)(124,204)(125,198)(126,197)(127,199)(128,200)
(129,226)(130,225)(131,227)(132,228)(133,238)(134,237)(135,239)(136,240)
(137,234)(138,233)(139,235)(140,236)(141,230)(142,229)(143,231)(144,232);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 13)( 6, 14)( 7, 16)
( 8, 15)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 29)( 22, 30)( 23, 32)
( 24, 31)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)
( 40, 47)( 49,105)( 50,106)( 51,108)( 52,107)( 53,109)( 54,110)( 55,112)
( 56,111)( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,101)( 62,102)( 63,104)
( 64,103)( 65,121)( 66,122)( 67,124)( 68,123)( 69,125)( 70,126)( 71,128)
( 72,127)( 73,113)( 74,114)( 75,116)( 76,115)( 77,117)( 78,118)( 79,120)
( 80,119)( 81,137)( 82,138)( 83,140)( 84,139)( 85,141)( 86,142)( 87,144)
( 88,143)( 89,129)( 90,130)( 91,132)( 92,131)( 93,133)( 94,134)( 95,136)
( 96,135)(145,153)(146,154)(147,156)(148,155)(149,157)(150,158)(151,160)
(152,159)(161,169)(162,170)(163,172)(164,171)(165,173)(166,174)(167,176)
(168,175)(177,185)(178,186)(179,188)(180,187)(181,189)(182,190)(183,192)
(184,191)(193,249)(194,250)(195,252)(196,251)(197,253)(198,254)(199,256)
(200,255)(201,241)(202,242)(203,244)(204,243)(205,245)(206,246)(207,248)
(208,247)(209,265)(210,266)(211,268)(212,267)(213,269)(214,270)(215,272)
(216,271)(217,257)(218,258)(219,260)(220,259)(221,261)(222,262)(223,264)
(224,263)(225,281)(226,282)(227,284)(228,283)(229,285)(230,286)(231,288)
(232,287)(233,273)(234,274)(235,276)(236,275)(237,277)(238,278)(239,280)
(240,279);
s1 := Sym(288)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 53)( 6, 56)( 7, 55)
( 8, 54)( 9, 61)( 10, 64)( 11, 63)( 12, 62)( 13, 57)( 14, 60)( 15, 59)
( 16, 58)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 85)( 22, 88)( 23, 87)
( 24, 86)( 25, 93)( 26, 96)( 27, 95)( 28, 94)( 29, 89)( 30, 92)( 31, 91)
( 32, 90)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 69)( 38, 72)( 39, 71)
( 40, 70)( 41, 77)( 42, 80)( 43, 79)( 44, 78)( 45, 73)( 46, 76)( 47, 75)
( 48, 74)( 98,100)(102,104)(105,109)(106,112)(107,111)(108,110)(113,129)
(114,132)(115,131)(116,130)(117,133)(118,136)(119,135)(120,134)(121,141)
(122,144)(123,143)(124,142)(125,137)(126,140)(127,139)(128,138)(145,193)
(146,196)(147,195)(148,194)(149,197)(150,200)(151,199)(152,198)(153,205)
(154,208)(155,207)(156,206)(157,201)(158,204)(159,203)(160,202)(161,225)
(162,228)(163,227)(164,226)(165,229)(166,232)(167,231)(168,230)(169,237)
(170,240)(171,239)(172,238)(173,233)(174,236)(175,235)(176,234)(177,209)
(178,212)(179,211)(180,210)(181,213)(182,216)(183,215)(184,214)(185,221)
(186,224)(187,223)(188,222)(189,217)(190,220)(191,219)(192,218)(242,244)
(246,248)(249,253)(250,256)(251,255)(252,254)(257,273)(258,276)(259,275)
(260,274)(261,277)(262,280)(263,279)(264,278)(265,285)(266,288)(267,287)
(268,286)(269,281)(270,284)(271,283)(272,282);
s2 := Sym(288)!( 1,162)( 2,161)( 3,163)( 4,164)( 5,174)( 6,173)( 7,175)
( 8,176)( 9,170)( 10,169)( 11,171)( 12,172)( 13,166)( 14,165)( 15,167)
( 16,168)( 17,146)( 18,145)( 19,147)( 20,148)( 21,158)( 22,157)( 23,159)
( 24,160)( 25,154)( 26,153)( 27,155)( 28,156)( 29,150)( 30,149)( 31,151)
( 32,152)( 33,178)( 34,177)( 35,179)( 36,180)( 37,190)( 38,189)( 39,191)
( 40,192)( 41,186)( 42,185)( 43,187)( 44,188)( 45,182)( 46,181)( 47,183)
( 48,184)( 49,258)( 50,257)( 51,259)( 52,260)( 53,270)( 54,269)( 55,271)
( 56,272)( 57,266)( 58,265)( 59,267)( 60,268)( 61,262)( 62,261)( 63,263)
( 64,264)( 65,242)( 66,241)( 67,243)( 68,244)( 69,254)( 70,253)( 71,255)
( 72,256)( 73,250)( 74,249)( 75,251)( 76,252)( 77,246)( 78,245)( 79,247)
( 80,248)( 81,274)( 82,273)( 83,275)( 84,276)( 85,286)( 86,285)( 87,287)
( 88,288)( 89,282)( 90,281)( 91,283)( 92,284)( 93,278)( 94,277)( 95,279)
( 96,280)( 97,210)( 98,209)( 99,211)(100,212)(101,222)(102,221)(103,223)
(104,224)(105,218)(106,217)(107,219)(108,220)(109,214)(110,213)(111,215)
(112,216)(113,194)(114,193)(115,195)(116,196)(117,206)(118,205)(119,207)
(120,208)(121,202)(122,201)(123,203)(124,204)(125,198)(126,197)(127,199)
(128,200)(129,226)(130,225)(131,227)(132,228)(133,238)(134,237)(135,239)
(136,240)(137,234)(138,233)(139,235)(140,236)(141,230)(142,229)(143,231)
(144,232);
poly := sub<Sym(288)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope