Polytope of Type {2,8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97554)
Rank : 4
Schlafli Type : {2,8,12}
Number of vertices, edges, etc : 2, 24, 144, 36
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 : {2,8,6}*576, {2,4,12}*576
   4-fold quotients : {2,4,6}*288
   8-fold quotients : {2,4,6}*144
   9-fold quotients : {2,8,4}*128a
   18-fold quotients : {2,4,4}*64, {2,8,2}*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 := (  3,147)(  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);;
s2 := (  6,  9)(  7, 10)(  8, 11)( 15, 18)( 16, 19)( 17, 20)( 24, 27)( 25, 28)
( 26, 29)( 33, 36)( 34, 37)( 35, 38)( 39, 48)( 40, 49)( 41, 50)( 42, 54)
( 43, 55)( 44, 56)( 45, 51)( 46, 52)( 47, 53)( 57, 66)( 58, 67)( 59, 68)
( 60, 72)( 61, 73)( 62, 74)( 63, 69)( 64, 70)( 65, 71)( 75, 93)( 76, 94)
( 77, 95)( 78, 99)( 79,100)( 80,101)( 81, 96)( 82, 97)( 83, 98)( 84,102)
( 85,103)( 86,104)( 87,108)( 88,109)( 89,110)( 90,105)( 91,106)( 92,107)
(111,138)(112,139)(113,140)(114,144)(115,145)(116,146)(117,141)(118,142)
(119,143)(120,129)(121,130)(122,131)(123,135)(124,136)(125,137)(126,132)
(127,133)(128,134)(147,183)(148,184)(149,185)(150,189)(151,190)(152,191)
(153,186)(154,187)(155,188)(156,192)(157,193)(158,194)(159,198)(160,199)
(161,200)(162,195)(163,196)(164,197)(165,201)(166,202)(167,203)(168,207)
(169,208)(170,209)(171,204)(172,205)(173,206)(174,210)(175,211)(176,212)
(177,216)(178,217)(179,218)(180,213)(181,214)(182,215)(219,273)(220,274)
(221,275)(222,279)(223,280)(224,281)(225,276)(226,277)(227,278)(228,282)
(229,283)(230,284)(231,288)(232,289)(233,290)(234,285)(235,286)(236,287)
(237,255)(238,256)(239,257)(240,261)(241,262)(242,263)(243,258)(244,259)
(245,260)(246,264)(247,265)(248,266)(249,270)(250,271)(251,272)(252,267)
(253,268)(254,269);;
s3 := (  3,115)(  4,114)(  5,116)(  6,112)(  7,111)(  8,113)(  9,118)( 10,117)
( 11,119)( 12,124)( 13,123)( 14,125)( 15,121)( 16,120)( 17,122)( 18,127)
( 19,126)( 20,128)( 21,133)( 22,132)( 23,134)( 24,130)( 25,129)( 26,131)
( 27,136)( 28,135)( 29,137)( 30,142)( 31,141)( 32,143)( 33,139)( 34,138)
( 35,140)( 36,145)( 37,144)( 38,146)( 39, 88)( 40, 87)( 41, 89)( 42, 85)
( 43, 84)( 44, 86)( 45, 91)( 46, 90)( 47, 92)( 48, 79)( 49, 78)( 50, 80)
( 51, 76)( 52, 75)( 53, 77)( 54, 82)( 55, 81)( 56, 83)( 57,106)( 58,105)
( 59,107)( 60,103)( 61,102)( 62,104)( 63,109)( 64,108)( 65,110)( 66, 97)
( 67, 96)( 68, 98)( 69, 94)( 70, 93)( 71, 95)( 72,100)( 73, 99)( 74,101)
(147,259)(148,258)(149,260)(150,256)(151,255)(152,257)(153,262)(154,261)
(155,263)(156,268)(157,267)(158,269)(159,265)(160,264)(161,266)(162,271)
(163,270)(164,272)(165,277)(166,276)(167,278)(168,274)(169,273)(170,275)
(171,280)(172,279)(173,281)(174,286)(175,285)(176,287)(177,283)(178,282)
(179,284)(180,289)(181,288)(182,290)(183,232)(184,231)(185,233)(186,229)
(187,228)(188,230)(189,235)(190,234)(191,236)(192,223)(193,222)(194,224)
(195,220)(196,219)(197,221)(198,226)(199,225)(200,227)(201,250)(202,249)
(203,251)(204,247)(205,246)(206,248)(207,253)(208,252)(209,254)(210,241)
(211,240)(212,242)(213,238)(214,237)(215,239)(216,244)(217,243)(218,245);;
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, 
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*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*s3*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(290)!(1,2);
s1 := 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);
s2 := Sym(290)!(  6,  9)(  7, 10)(  8, 11)( 15, 18)( 16, 19)( 17, 20)( 24, 27)
( 25, 28)( 26, 29)( 33, 36)( 34, 37)( 35, 38)( 39, 48)( 40, 49)( 41, 50)
( 42, 54)( 43, 55)( 44, 56)( 45, 51)( 46, 52)( 47, 53)( 57, 66)( 58, 67)
( 59, 68)( 60, 72)( 61, 73)( 62, 74)( 63, 69)( 64, 70)( 65, 71)( 75, 93)
( 76, 94)( 77, 95)( 78, 99)( 79,100)( 80,101)( 81, 96)( 82, 97)( 83, 98)
( 84,102)( 85,103)( 86,104)( 87,108)( 88,109)( 89,110)( 90,105)( 91,106)
( 92,107)(111,138)(112,139)(113,140)(114,144)(115,145)(116,146)(117,141)
(118,142)(119,143)(120,129)(121,130)(122,131)(123,135)(124,136)(125,137)
(126,132)(127,133)(128,134)(147,183)(148,184)(149,185)(150,189)(151,190)
(152,191)(153,186)(154,187)(155,188)(156,192)(157,193)(158,194)(159,198)
(160,199)(161,200)(162,195)(163,196)(164,197)(165,201)(166,202)(167,203)
(168,207)(169,208)(170,209)(171,204)(172,205)(173,206)(174,210)(175,211)
(176,212)(177,216)(178,217)(179,218)(180,213)(181,214)(182,215)(219,273)
(220,274)(221,275)(222,279)(223,280)(224,281)(225,276)(226,277)(227,278)
(228,282)(229,283)(230,284)(231,288)(232,289)(233,290)(234,285)(235,286)
(236,287)(237,255)(238,256)(239,257)(240,261)(241,262)(242,263)(243,258)
(244,259)(245,260)(246,264)(247,265)(248,266)(249,270)(250,271)(251,272)
(252,267)(253,268)(254,269);
s3 := Sym(290)!(  3,115)(  4,114)(  5,116)(  6,112)(  7,111)(  8,113)(  9,118)
( 10,117)( 11,119)( 12,124)( 13,123)( 14,125)( 15,121)( 16,120)( 17,122)
( 18,127)( 19,126)( 20,128)( 21,133)( 22,132)( 23,134)( 24,130)( 25,129)
( 26,131)( 27,136)( 28,135)( 29,137)( 30,142)( 31,141)( 32,143)( 33,139)
( 34,138)( 35,140)( 36,145)( 37,144)( 38,146)( 39, 88)( 40, 87)( 41, 89)
( 42, 85)( 43, 84)( 44, 86)( 45, 91)( 46, 90)( 47, 92)( 48, 79)( 49, 78)
( 50, 80)( 51, 76)( 52, 75)( 53, 77)( 54, 82)( 55, 81)( 56, 83)( 57,106)
( 58,105)( 59,107)( 60,103)( 61,102)( 62,104)( 63,109)( 64,108)( 65,110)
( 66, 97)( 67, 96)( 68, 98)( 69, 94)( 70, 93)( 71, 95)( 72,100)( 73, 99)
( 74,101)(147,259)(148,258)(149,260)(150,256)(151,255)(152,257)(153,262)
(154,261)(155,263)(156,268)(157,267)(158,269)(159,265)(160,264)(161,266)
(162,271)(163,270)(164,272)(165,277)(166,276)(167,278)(168,274)(169,273)
(170,275)(171,280)(172,279)(173,281)(174,286)(175,285)(176,287)(177,283)
(178,282)(179,284)(180,289)(181,288)(182,290)(183,232)(184,231)(185,233)
(186,229)(187,228)(188,230)(189,235)(190,234)(191,236)(192,223)(193,222)
(194,224)(195,220)(196,219)(197,221)(198,226)(199,225)(200,227)(201,250)
(202,249)(203,251)(204,247)(205,246)(206,248)(207,253)(208,252)(209,254)
(210,241)(211,240)(212,242)(213,238)(214,237)(215,239)(216,244)(217,243)
(218,245);
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, s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*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*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;

to this polytope