Polytope of Type {36,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,8}*1152g
if this polytope has a name.
Group : SmallGroup(1152,154295)
Rank : 3
Schlafli Type : {36,8}
Number of vertices, edges, etc : 72, 288, 16
Order of s₀s₁s₂ : 18
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {36,4}*576c, {18,8}*576c
   3-fold quotients : {12,8}*384g
   4-fold quotients : {18,4}*288
   6-fold quotients : {12,4}*192c, {6,8}*192c
   8-fold quotients : {9,4}*144, {18,4}*144b, {18,4}*144c
   12-fold quotients : {6,4}*96
   16-fold quotients : {9,4}*72, {18,2}*72
   24-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {9,2}*36
   48-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {3,2}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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