Polytope of Type {2,16,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,133456)
Rank : 4
Schlafli Type : {2,16,6}
Number of vertices, edges, etc : 2, 48, 144, 18
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 : {2,8,6}*576
   4-fold quotients : {2,4,6}*288
   8-fold quotients : {2,4,6}*144
   9-fold quotients : {2,16,2}*128
   18-fold quotients : {2,8,2}*64
   36-fold quotients : {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 := (  6,  9)(  7, 10)(  8, 11)( 15, 18)( 16, 19)( 17, 20)( 21, 30)( 22, 31)
( 23, 32)( 24, 36)( 25, 37)( 26, 38)( 27, 33)( 28, 34)( 29, 35)( 39, 57)
( 40, 58)( 41, 59)( 42, 63)( 43, 64)( 44, 65)( 45, 60)( 46, 61)( 47, 62)
( 48, 66)( 49, 67)( 50, 68)( 51, 72)( 52, 73)( 53, 74)( 54, 69)( 55, 70)
( 56, 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)(111,120)(112,121)(113,122)(114,126)(115,127)
(116,128)(117,123)(118,124)(119,125)(132,135)(133,136)(134,137)(141,144)
(142,145)(143,146)(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)(165,210)(166,211)(167,212)(168,216)
(169,217)(170,218)(171,213)(172,214)(173,215)(174,201)(175,202)(176,203)
(177,207)(178,208)(179,209)(180,204)(181,205)(182,206)(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);;
s2 := (  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);;
s3 := (  3,130)(  4,129)(  5,131)(  6,136)(  7,135)(  8,137)(  9,133)( 10,132)
( 11,134)( 12,139)( 13,138)( 14,140)( 15,145)( 16,144)( 17,146)( 18,142)
( 19,141)( 20,143)( 21,121)( 22,120)( 23,122)( 24,127)( 25,126)( 26,128)
( 27,124)( 28,123)( 29,125)( 30,112)( 31,111)( 32,113)( 33,118)( 34,117)
( 35,119)( 36,115)( 37,114)( 38,116)( 39, 76)( 40, 75)( 41, 77)( 42, 82)
( 43, 81)( 44, 83)( 45, 79)( 46, 78)( 47, 80)( 48, 85)( 49, 84)( 50, 86)
( 51, 91)( 52, 90)( 53, 92)( 54, 88)( 55, 87)( 56, 89)( 57, 94)( 58, 93)
( 59, 95)( 60,100)( 61, 99)( 62,101)( 63, 97)( 64, 96)( 65, 98)( 66,103)
( 67,102)( 68,104)( 69,109)( 70,108)( 71,110)( 72,106)( 73,105)( 74,107)
(147,274)(148,273)(149,275)(150,280)(151,279)(152,281)(153,277)(154,276)
(155,278)(156,283)(157,282)(158,284)(159,289)(160,288)(161,290)(162,286)
(163,285)(164,287)(165,265)(166,264)(167,266)(168,271)(169,270)(170,272)
(171,268)(172,267)(173,269)(174,256)(175,255)(176,257)(177,262)(178,261)
(179,263)(180,259)(181,258)(182,260)(183,220)(184,219)(185,221)(186,226)
(187,225)(188,227)(189,223)(190,222)(191,224)(192,229)(193,228)(194,230)
(195,235)(196,234)(197,236)(198,232)(199,231)(200,233)(201,238)(202,237)
(203,239)(204,244)(205,243)(206,245)(207,241)(208,240)(209,242)(210,247)
(211,246)(212,248)(213,253)(214,252)(215,254)(216,250)(217,249)(218,251);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope