Polytope of Type {2,6,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,16}*1152
if this polytope has a name.
Group : SmallGroup(1152,133456)
Rank : 4
Schlafli Type : {2,6,16}
Number of vertices, edges, etc : 2, 18, 144, 48
Order of s₀s₁s₂s₃ : 16
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
   4-fold quotients : {2,6,4}*288
   8-fold quotients : {2,6,4}*144
   9-fold quotients : {2,2,16}*128
   18-fold quotients : {2,2,8}*64
   36-fold quotients : {2,2,4}*32
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3,129)(  4,131)(  5,130)(  6,135)(  7,137)(  8,136)(  9,132)( 10,134)
( 11,133)( 12,138)( 13,140)( 14,139)( 15,144)( 16,146)( 17,145)( 18,141)
( 19,143)( 20,142)( 21,120)( 22,122)( 23,121)( 24,126)( 25,128)( 26,127)
( 27,123)( 28,125)( 29,124)( 30,111)( 31,113)( 32,112)( 33,117)( 34,119)
( 35,118)( 36,114)( 37,116)( 38,115)( 39, 75)( 40, 77)( 41, 76)( 42, 81)
( 43, 83)( 44, 82)( 45, 78)( 46, 80)( 47, 79)( 48, 84)( 49, 86)( 50, 85)
( 51, 90)( 52, 92)( 53, 91)( 54, 87)( 55, 89)( 56, 88)( 57, 93)( 58, 95)
( 59, 94)( 60, 99)( 61,101)( 62,100)( 63, 96)( 64, 98)( 65, 97)( 66,102)
( 67,104)( 68,103)( 69,108)( 70,110)( 71,109)( 72,105)( 73,107)( 74,106)
(147,273)(148,275)(149,274)(150,279)(151,281)(152,280)(153,276)(154,278)
(155,277)(156,282)(157,284)(158,283)(159,288)(160,290)(161,289)(162,285)
(163,287)(164,286)(165,264)(166,266)(167,265)(168,270)(169,272)(170,271)
(171,267)(172,269)(173,268)(174,255)(175,257)(176,256)(177,261)(178,263)
(179,262)(180,258)(181,260)(182,259)(183,219)(184,221)(185,220)(186,225)
(187,227)(188,226)(189,222)(190,224)(191,223)(192,228)(193,230)(194,229)
(195,234)(196,236)(197,235)(198,231)(199,233)(200,232)(201,237)(202,239)
(203,238)(204,243)(205,245)(206,244)(207,240)(208,242)(209,241)(210,246)
(211,248)(212,247)(213,252)(214,254)(215,253)(216,249)(217,251)(218,250);;
s2 := (  3,  6)(  4,  7)(  5,  8)( 12, 15)( 13, 16)( 14, 17)( 21, 33)( 22, 34)
( 23, 35)( 24, 30)( 25, 31)( 26, 32)( 27, 36)( 28, 37)( 29, 38)( 39, 60)
( 40, 61)( 41, 62)( 42, 57)( 43, 58)( 44, 59)( 45, 63)( 46, 64)( 47, 65)
( 48, 69)( 49, 70)( 50, 71)( 51, 66)( 52, 67)( 53, 68)( 54, 72)( 55, 73)
( 56, 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)(111,123)(112,124)(113,125)(114,120)(115,121)
(116,122)(117,126)(118,127)(119,128)(129,132)(130,133)(131,134)(138,141)
(139,142)(140,143)(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)(165,213)(166,214)(167,215)(168,210)
(169,211)(170,212)(171,216)(172,217)(173,218)(174,204)(175,205)(176,206)
(177,201)(178,202)(179,203)(180,207)(181,208)(182,209)(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)( 21,174)( 22,177)( 23,180)( 24,175)( 25,178)( 26,181)
( 27,176)( 28,179)( 29,182)( 30,165)( 31,168)( 32,171)( 33,166)( 34,169)
( 35,172)( 36,167)( 37,170)( 38,173)( 39,201)( 40,204)( 41,207)( 42,202)
( 43,205)( 44,208)( 45,203)( 46,206)( 47,209)( 48,210)( 49,213)( 50,216)
( 51,211)( 52,214)( 53,217)( 54,212)( 55,215)( 56,218)( 57,183)( 58,186)
( 59,189)( 60,184)( 61,187)( 62,190)( 63,185)( 64,188)( 65,191)( 66,192)
( 67,195)( 68,198)( 69,193)( 70,196)( 71,199)( 72,194)( 73,197)( 74,200)
( 75,237)( 76,240)( 77,243)( 78,238)( 79,241)( 80,244)( 81,239)( 82,242)
( 83,245)( 84,246)( 85,249)( 86,252)( 87,247)( 88,250)( 89,253)( 90,248)
( 91,251)( 92,254)( 93,219)( 94,222)( 95,225)( 96,220)( 97,223)( 98,226)
( 99,221)(100,224)(101,227)(102,228)(103,231)(104,234)(105,229)(106,232)
(107,235)(108,230)(109,233)(110,236)(111,264)(112,267)(113,270)(114,265)
(115,268)(116,271)(117,266)(118,269)(119,272)(120,255)(121,258)(122,261)
(123,256)(124,259)(125,262)(126,257)(127,260)(128,263)(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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(290)!(1,2);
s1 := Sym(290)!(  3,129)(  4,131)(  5,130)(  6,135)(  7,137)(  8,136)(  9,132)
( 10,134)( 11,133)( 12,138)( 13,140)( 14,139)( 15,144)( 16,146)( 17,145)
( 18,141)( 19,143)( 20,142)( 21,120)( 22,122)( 23,121)( 24,126)( 25,128)
( 26,127)( 27,123)( 28,125)( 29,124)( 30,111)( 31,113)( 32,112)( 33,117)
( 34,119)( 35,118)( 36,114)( 37,116)( 38,115)( 39, 75)( 40, 77)( 41, 76)
( 42, 81)( 43, 83)( 44, 82)( 45, 78)( 46, 80)( 47, 79)( 48, 84)( 49, 86)
( 50, 85)( 51, 90)( 52, 92)( 53, 91)( 54, 87)( 55, 89)( 56, 88)( 57, 93)
( 58, 95)( 59, 94)( 60, 99)( 61,101)( 62,100)( 63, 96)( 64, 98)( 65, 97)
( 66,102)( 67,104)( 68,103)( 69,108)( 70,110)( 71,109)( 72,105)( 73,107)
( 74,106)(147,273)(148,275)(149,274)(150,279)(151,281)(152,280)(153,276)
(154,278)(155,277)(156,282)(157,284)(158,283)(159,288)(160,290)(161,289)
(162,285)(163,287)(164,286)(165,264)(166,266)(167,265)(168,270)(169,272)
(170,271)(171,267)(172,269)(173,268)(174,255)(175,257)(176,256)(177,261)
(178,263)(179,262)(180,258)(181,260)(182,259)(183,219)(184,221)(185,220)
(186,225)(187,227)(188,226)(189,222)(190,224)(191,223)(192,228)(193,230)
(194,229)(195,234)(196,236)(197,235)(198,231)(199,233)(200,232)(201,237)
(202,239)(203,238)(204,243)(205,245)(206,244)(207,240)(208,242)(209,241)
(210,246)(211,248)(212,247)(213,252)(214,254)(215,253)(216,249)(217,251)
(218,250);
s2 := Sym(290)!(  3,  6)(  4,  7)(  5,  8)( 12, 15)( 13, 16)( 14, 17)( 21, 33)
( 22, 34)( 23, 35)( 24, 30)( 25, 31)( 26, 32)( 27, 36)( 28, 37)( 29, 38)
( 39, 60)( 40, 61)( 41, 62)( 42, 57)( 43, 58)( 44, 59)( 45, 63)( 46, 64)
( 47, 65)( 48, 69)( 49, 70)( 50, 71)( 51, 66)( 52, 67)( 53, 68)( 54, 72)
( 55, 73)( 56, 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)(111,123)(112,124)(113,125)(114,120)
(115,121)(116,122)(117,126)(118,127)(119,128)(129,132)(130,133)(131,134)
(138,141)(139,142)(140,143)(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)(165,213)(166,214)(167,215)
(168,210)(169,211)(170,212)(171,216)(172,217)(173,218)(174,204)(175,205)
(176,206)(177,201)(178,202)(179,203)(180,207)(181,208)(182,209)(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)( 21,174)( 22,177)( 23,180)( 24,175)( 25,178)
( 26,181)( 27,176)( 28,179)( 29,182)( 30,165)( 31,168)( 32,171)( 33,166)
( 34,169)( 35,172)( 36,167)( 37,170)( 38,173)( 39,201)( 40,204)( 41,207)
( 42,202)( 43,205)( 44,208)( 45,203)( 46,206)( 47,209)( 48,210)( 49,213)
( 50,216)( 51,211)( 52,214)( 53,217)( 54,212)( 55,215)( 56,218)( 57,183)
( 58,186)( 59,189)( 60,184)( 61,187)( 62,190)( 63,185)( 64,188)( 65,191)
( 66,192)( 67,195)( 68,198)( 69,193)( 70,196)( 71,199)( 72,194)( 73,197)
( 74,200)( 75,237)( 76,240)( 77,243)( 78,238)( 79,241)( 80,244)( 81,239)
( 82,242)( 83,245)( 84,246)( 85,249)( 86,252)( 87,247)( 88,250)( 89,253)
( 90,248)( 91,251)( 92,254)( 93,219)( 94,222)( 95,225)( 96,220)( 97,223)
( 98,226)( 99,221)(100,224)(101,227)(102,228)(103,231)(104,234)(105,229)
(106,232)(107,235)(108,230)(109,233)(110,236)(111,264)(112,267)(113,270)
(114,265)(115,268)(116,271)(117,266)(118,269)(119,272)(120,255)(121,258)
(122,261)(123,256)(124,259)(125,262)(126,257)(127,260)(128,263)(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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope