Polytope of Type {2,12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,8}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97554)
Rank : 4
Schlafli Type : {2,12,8}
Number of vertices, edges, etc : 2, 36, 144, 24
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,6,8}*576, {2,12,4}*576
4-fold quotients : {2,6,4}*288
8-fold quotients : {2,6,4}*144
9-fold quotients : {2,4,8}*128a
18-fold quotients : {2,4,4}*64, {2,2,8}*64
36-fold quotients : {2,2,4}*32, {2,4,2}*32
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,111)( 4,113)( 5,112)( 6,117)( 7,119)( 8,118)( 9,114)( 10,116)
( 11,115)( 12,120)( 13,122)( 14,121)( 15,126)( 16,128)( 17,127)( 18,123)
( 19,125)( 20,124)( 21,129)( 22,131)( 23,130)( 24,135)( 25,137)( 26,136)
( 27,132)( 28,134)( 29,133)( 30,138)( 31,140)( 32,139)( 33,144)( 34,146)
( 35,145)( 36,141)( 37,143)( 38,142)( 39, 84)( 40, 86)( 41, 85)( 42, 90)
( 43, 92)( 44, 91)( 45, 87)( 46, 89)( 47, 88)( 48, 75)( 49, 77)( 50, 76)
( 51, 81)( 52, 83)( 53, 82)( 54, 78)( 55, 80)( 56, 79)( 57,102)( 58,104)
( 59,103)( 60,108)( 61,110)( 62,109)( 63,105)( 64,107)( 65,106)( 66, 93)
( 67, 95)( 68, 94)( 69, 99)( 70,101)( 71,100)( 72, 96)( 73, 98)( 74, 97)
(147,255)(148,257)(149,256)(150,261)(151,263)(152,262)(153,258)(154,260)
(155,259)(156,264)(157,266)(158,265)(159,270)(160,272)(161,271)(162,267)
(163,269)(164,268)(165,273)(166,275)(167,274)(168,279)(169,281)(170,280)
(171,276)(172,278)(173,277)(174,282)(175,284)(176,283)(177,288)(178,290)
(179,289)(180,285)(181,287)(182,286)(183,228)(184,230)(185,229)(186,234)
(187,236)(188,235)(189,231)(190,233)(191,232)(192,219)(193,221)(194,220)
(195,225)(196,227)(197,226)(198,222)(199,224)(200,223)(201,246)(202,248)
(203,247)(204,252)(205,254)(206,253)(207,249)(208,251)(209,250)(210,237)
(211,239)(212,238)(213,243)(214,245)(215,244)(216,240)(217,242)(218,241);;
s2 := ( 3, 6)( 4, 7)( 5, 8)( 12, 15)( 13, 16)( 14, 17)( 21, 24)( 22, 25)
( 23, 26)( 30, 33)( 31, 34)( 32, 35)( 39, 51)( 40, 52)( 41, 53)( 42, 48)
( 43, 49)( 44, 50)( 45, 54)( 46, 55)( 47, 56)( 57, 69)( 58, 70)( 59, 71)
( 60, 66)( 61, 67)( 62, 68)( 63, 72)( 64, 73)( 65, 74)( 75, 96)( 76, 97)
( 77, 98)( 78, 93)( 79, 94)( 80, 95)( 81, 99)( 82,100)( 83,101)( 84,105)
( 85,106)( 86,107)( 87,102)( 88,103)( 89,104)( 90,108)( 91,109)( 92,110)
(111,141)(112,142)(113,143)(114,138)(115,139)(116,140)(117,144)(118,145)
(119,146)(120,132)(121,133)(122,134)(123,129)(124,130)(125,131)(126,135)
(127,136)(128,137)(147,186)(148,187)(149,188)(150,183)(151,184)(152,185)
(153,189)(154,190)(155,191)(156,195)(157,196)(158,197)(159,192)(160,193)
(161,194)(162,198)(163,199)(164,200)(165,204)(166,205)(167,206)(168,201)
(169,202)(170,203)(171,207)(172,208)(173,209)(174,213)(175,214)(176,215)
(177,210)(178,211)(179,212)(180,216)(181,217)(182,218)(219,276)(220,277)
(221,278)(222,273)(223,274)(224,275)(225,279)(226,280)(227,281)(228,285)
(229,286)(230,287)(231,282)(232,283)(233,284)(234,288)(235,289)(236,290)
(237,258)(238,259)(239,260)(240,255)(241,256)(242,257)(243,261)(244,262)
(245,263)(246,267)(247,268)(248,269)(249,264)(250,265)(251,266)(252,270)
(253,271)(254,272);;
s3 := ( 3,147)( 4,150)( 5,153)( 6,148)( 7,151)( 8,154)( 9,149)( 10,152)
( 11,155)( 12,156)( 13,159)( 14,162)( 15,157)( 16,160)( 17,163)( 18,158)
( 19,161)( 20,164)( 21,165)( 22,168)( 23,171)( 24,166)( 25,169)( 26,172)
( 27,167)( 28,170)( 29,173)( 30,174)( 31,177)( 32,180)( 33,175)( 34,178)
( 35,181)( 36,176)( 37,179)( 38,182)( 39,192)( 40,195)( 41,198)( 42,193)
( 43,196)( 44,199)( 45,194)( 46,197)( 47,200)( 48,183)( 49,186)( 50,189)
( 51,184)( 52,187)( 53,190)( 54,185)( 55,188)( 56,191)( 57,210)( 58,213)
( 59,216)( 60,211)( 61,214)( 62,217)( 63,212)( 64,215)( 65,218)( 66,201)
( 67,204)( 68,207)( 69,202)( 70,205)( 71,208)( 72,203)( 73,206)( 74,209)
( 75,228)( 76,231)( 77,234)( 78,229)( 79,232)( 80,235)( 81,230)( 82,233)
( 83,236)( 84,219)( 85,222)( 86,225)( 87,220)( 88,223)( 89,226)( 90,221)
( 91,224)( 92,227)( 93,246)( 94,249)( 95,252)( 96,247)( 97,250)( 98,253)
( 99,248)(100,251)(101,254)(102,237)(103,240)(104,243)(105,238)(106,241)
(107,244)(108,239)(109,242)(110,245)(111,255)(112,258)(113,261)(114,256)
(115,259)(116,262)(117,257)(118,260)(119,263)(120,264)(121,267)(122,270)
(123,265)(124,268)(125,271)(126,266)(127,269)(128,272)(129,273)(130,276)
(131,279)(132,274)(133,277)(134,280)(135,275)(136,278)(137,281)(138,282)
(139,285)(140,288)(141,283)(142,286)(143,289)(144,284)(145,287)(146,290);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(290)!(1,2);
s1 := Sym(290)!( 3,111)( 4,113)( 5,112)( 6,117)( 7,119)( 8,118)( 9,114)
( 10,116)( 11,115)( 12,120)( 13,122)( 14,121)( 15,126)( 16,128)( 17,127)
( 18,123)( 19,125)( 20,124)( 21,129)( 22,131)( 23,130)( 24,135)( 25,137)
( 26,136)( 27,132)( 28,134)( 29,133)( 30,138)( 31,140)( 32,139)( 33,144)
( 34,146)( 35,145)( 36,141)( 37,143)( 38,142)( 39, 84)( 40, 86)( 41, 85)
( 42, 90)( 43, 92)( 44, 91)( 45, 87)( 46, 89)( 47, 88)( 48, 75)( 49, 77)
( 50, 76)( 51, 81)( 52, 83)( 53, 82)( 54, 78)( 55, 80)( 56, 79)( 57,102)
( 58,104)( 59,103)( 60,108)( 61,110)( 62,109)( 63,105)( 64,107)( 65,106)
( 66, 93)( 67, 95)( 68, 94)( 69, 99)( 70,101)( 71,100)( 72, 96)( 73, 98)
( 74, 97)(147,255)(148,257)(149,256)(150,261)(151,263)(152,262)(153,258)
(154,260)(155,259)(156,264)(157,266)(158,265)(159,270)(160,272)(161,271)
(162,267)(163,269)(164,268)(165,273)(166,275)(167,274)(168,279)(169,281)
(170,280)(171,276)(172,278)(173,277)(174,282)(175,284)(176,283)(177,288)
(178,290)(179,289)(180,285)(181,287)(182,286)(183,228)(184,230)(185,229)
(186,234)(187,236)(188,235)(189,231)(190,233)(191,232)(192,219)(193,221)
(194,220)(195,225)(196,227)(197,226)(198,222)(199,224)(200,223)(201,246)
(202,248)(203,247)(204,252)(205,254)(206,253)(207,249)(208,251)(209,250)
(210,237)(211,239)(212,238)(213,243)(214,245)(215,244)(216,240)(217,242)
(218,241);
s2 := Sym(290)!( 3, 6)( 4, 7)( 5, 8)( 12, 15)( 13, 16)( 14, 17)( 21, 24)
( 22, 25)( 23, 26)( 30, 33)( 31, 34)( 32, 35)( 39, 51)( 40, 52)( 41, 53)
( 42, 48)( 43, 49)( 44, 50)( 45, 54)( 46, 55)( 47, 56)( 57, 69)( 58, 70)
( 59, 71)( 60, 66)( 61, 67)( 62, 68)( 63, 72)( 64, 73)( 65, 74)( 75, 96)
( 76, 97)( 77, 98)( 78, 93)( 79, 94)( 80, 95)( 81, 99)( 82,100)( 83,101)
( 84,105)( 85,106)( 86,107)( 87,102)( 88,103)( 89,104)( 90,108)( 91,109)
( 92,110)(111,141)(112,142)(113,143)(114,138)(115,139)(116,140)(117,144)
(118,145)(119,146)(120,132)(121,133)(122,134)(123,129)(124,130)(125,131)
(126,135)(127,136)(128,137)(147,186)(148,187)(149,188)(150,183)(151,184)
(152,185)(153,189)(154,190)(155,191)(156,195)(157,196)(158,197)(159,192)
(160,193)(161,194)(162,198)(163,199)(164,200)(165,204)(166,205)(167,206)
(168,201)(169,202)(170,203)(171,207)(172,208)(173,209)(174,213)(175,214)
(176,215)(177,210)(178,211)(179,212)(180,216)(181,217)(182,218)(219,276)
(220,277)(221,278)(222,273)(223,274)(224,275)(225,279)(226,280)(227,281)
(228,285)(229,286)(230,287)(231,282)(232,283)(233,284)(234,288)(235,289)
(236,290)(237,258)(238,259)(239,260)(240,255)(241,256)(242,257)(243,261)
(244,262)(245,263)(246,267)(247,268)(248,269)(249,264)(250,265)(251,266)
(252,270)(253,271)(254,272);
s3 := Sym(290)!( 3,147)( 4,150)( 5,153)( 6,148)( 7,151)( 8,154)( 9,149)
( 10,152)( 11,155)( 12,156)( 13,159)( 14,162)( 15,157)( 16,160)( 17,163)
( 18,158)( 19,161)( 20,164)( 21,165)( 22,168)( 23,171)( 24,166)( 25,169)
( 26,172)( 27,167)( 28,170)( 29,173)( 30,174)( 31,177)( 32,180)( 33,175)
( 34,178)( 35,181)( 36,176)( 37,179)( 38,182)( 39,192)( 40,195)( 41,198)
( 42,193)( 43,196)( 44,199)( 45,194)( 46,197)( 47,200)( 48,183)( 49,186)
( 50,189)( 51,184)( 52,187)( 53,190)( 54,185)( 55,188)( 56,191)( 57,210)
( 58,213)( 59,216)( 60,211)( 61,214)( 62,217)( 63,212)( 64,215)( 65,218)
( 66,201)( 67,204)( 68,207)( 69,202)( 70,205)( 71,208)( 72,203)( 73,206)
( 74,209)( 75,228)( 76,231)( 77,234)( 78,229)( 79,232)( 80,235)( 81,230)
( 82,233)( 83,236)( 84,219)( 85,222)( 86,225)( 87,220)( 88,223)( 89,226)
( 90,221)( 91,224)( 92,227)( 93,246)( 94,249)( 95,252)( 96,247)( 97,250)
( 98,253)( 99,248)(100,251)(101,254)(102,237)(103,240)(104,243)(105,238)
(106,241)(107,244)(108,239)(109,242)(110,245)(111,255)(112,258)(113,261)
(114,256)(115,259)(116,262)(117,257)(118,260)(119,263)(120,264)(121,267)
(122,270)(123,265)(124,268)(125,271)(126,266)(127,269)(128,272)(129,273)
(130,276)(131,279)(132,274)(133,277)(134,280)(135,275)(136,278)(137,281)
(138,282)(139,285)(140,288)(141,283)(142,286)(143,289)(144,284)(145,287)
(146,290);
poly := sub<Sym(290)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope