Polytope of Type {236}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {236}*472
Also Known As : 236-gon, {236}. if this polytope has another name.
Group : SmallGroup(472,5)
Rank : 2
Schlafli Type : {236}
Number of vertices, edges, etc : 236, 236
Order of s0s1 : 236
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {236,2} of size 944
   {236,4} of size 1888
Vertex Figure Of :
   {2,236} of size 944
   {4,236} of size 1888
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {118}*236
   4-fold quotients : {59}*118
   59-fold quotients : {4}*8
   118-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {472}*944
   3-fold covers : {708}*1416
   4-fold covers : {944}*1888
Permutation Representation (GAP) :
s0 := (  2, 59)(  3, 58)(  4, 57)(  5, 56)(  6, 55)(  7, 54)(  8, 53)(  9, 52)
( 10, 51)( 11, 50)( 12, 49)( 13, 48)( 14, 47)( 15, 46)( 16, 45)( 17, 44)
( 18, 43)( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 38)( 24, 37)( 25, 36)
( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 61,118)( 62,117)( 63,116)
( 64,115)( 65,114)( 66,113)( 67,112)( 68,111)( 69,110)( 70,109)( 71,108)
( 72,107)( 73,106)( 74,105)( 75,104)( 76,103)( 77,102)( 78,101)( 79,100)
( 80, 99)( 81, 98)( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)
( 88, 91)( 89, 90)(119,178)(120,236)(121,235)(122,234)(123,233)(124,232)
(125,231)(126,230)(127,229)(128,228)(129,227)(130,226)(131,225)(132,224)
(133,223)(134,222)(135,221)(136,220)(137,219)(138,218)(139,217)(140,216)
(141,215)(142,214)(143,213)(144,212)(145,211)(146,210)(147,209)(148,208)
(149,207)(150,206)(151,205)(152,204)(153,203)(154,202)(155,201)(156,200)
(157,199)(158,198)(159,197)(160,196)(161,195)(162,194)(163,193)(164,192)
(165,191)(166,190)(167,189)(168,188)(169,187)(170,186)(171,185)(172,184)
(173,183)(174,182)(175,181)(176,180)(177,179);;
s1 := (  1,120)(  2,119)(  3,177)(  4,176)(  5,175)(  6,174)(  7,173)(  8,172)
(  9,171)( 10,170)( 11,169)( 12,168)( 13,167)( 14,166)( 15,165)( 16,164)
( 17,163)( 18,162)( 19,161)( 20,160)( 21,159)( 22,158)( 23,157)( 24,156)
( 25,155)( 26,154)( 27,153)( 28,152)( 29,151)( 30,150)( 31,149)( 32,148)
( 33,147)( 34,146)( 35,145)( 36,144)( 37,143)( 38,142)( 39,141)( 40,140)
( 41,139)( 42,138)( 43,137)( 44,136)( 45,135)( 46,134)( 47,133)( 48,132)
( 49,131)( 50,130)( 51,129)( 52,128)( 53,127)( 54,126)( 55,125)( 56,124)
( 57,123)( 58,122)( 59,121)( 60,179)( 61,178)( 62,236)( 63,235)( 64,234)
( 65,233)( 66,232)( 67,231)( 68,230)( 69,229)( 70,228)( 71,227)( 72,226)
( 73,225)( 74,224)( 75,223)( 76,222)( 77,221)( 78,220)( 79,219)( 80,218)
( 81,217)( 82,216)( 83,215)( 84,214)( 85,213)( 86,212)( 87,211)( 88,210)
( 89,209)( 90,208)( 91,207)( 92,206)( 93,205)( 94,204)( 95,203)( 96,202)
( 97,201)( 98,200)( 99,199)(100,198)(101,197)(102,196)(103,195)(104,194)
(105,193)(106,192)(107,191)(108,190)(109,189)(110,188)(111,187)(112,186)
(113,185)(114,184)(115,183)(116,182)(117,181)(118,180);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(236)!(  2, 59)(  3, 58)(  4, 57)(  5, 56)(  6, 55)(  7, 54)(  8, 53)
(  9, 52)( 10, 51)( 11, 50)( 12, 49)( 13, 48)( 14, 47)( 15, 46)( 16, 45)
( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 38)( 24, 37)
( 25, 36)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 61,118)( 62,117)
( 63,116)( 64,115)( 65,114)( 66,113)( 67,112)( 68,111)( 69,110)( 70,109)
( 71,108)( 72,107)( 73,106)( 74,105)( 75,104)( 76,103)( 77,102)( 78,101)
( 79,100)( 80, 99)( 81, 98)( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)
( 87, 92)( 88, 91)( 89, 90)(119,178)(120,236)(121,235)(122,234)(123,233)
(124,232)(125,231)(126,230)(127,229)(128,228)(129,227)(130,226)(131,225)
(132,224)(133,223)(134,222)(135,221)(136,220)(137,219)(138,218)(139,217)
(140,216)(141,215)(142,214)(143,213)(144,212)(145,211)(146,210)(147,209)
(148,208)(149,207)(150,206)(151,205)(152,204)(153,203)(154,202)(155,201)
(156,200)(157,199)(158,198)(159,197)(160,196)(161,195)(162,194)(163,193)
(164,192)(165,191)(166,190)(167,189)(168,188)(169,187)(170,186)(171,185)
(172,184)(173,183)(174,182)(175,181)(176,180)(177,179);
s1 := Sym(236)!(  1,120)(  2,119)(  3,177)(  4,176)(  5,175)(  6,174)(  7,173)
(  8,172)(  9,171)( 10,170)( 11,169)( 12,168)( 13,167)( 14,166)( 15,165)
( 16,164)( 17,163)( 18,162)( 19,161)( 20,160)( 21,159)( 22,158)( 23,157)
( 24,156)( 25,155)( 26,154)( 27,153)( 28,152)( 29,151)( 30,150)( 31,149)
( 32,148)( 33,147)( 34,146)( 35,145)( 36,144)( 37,143)( 38,142)( 39,141)
( 40,140)( 41,139)( 42,138)( 43,137)( 44,136)( 45,135)( 46,134)( 47,133)
( 48,132)( 49,131)( 50,130)( 51,129)( 52,128)( 53,127)( 54,126)( 55,125)
( 56,124)( 57,123)( 58,122)( 59,121)( 60,179)( 61,178)( 62,236)( 63,235)
( 64,234)( 65,233)( 66,232)( 67,231)( 68,230)( 69,229)( 70,228)( 71,227)
( 72,226)( 73,225)( 74,224)( 75,223)( 76,222)( 77,221)( 78,220)( 79,219)
( 80,218)( 81,217)( 82,216)( 83,215)( 84,214)( 85,213)( 86,212)( 87,211)
( 88,210)( 89,209)( 90,208)( 91,207)( 92,206)( 93,205)( 94,204)( 95,203)
( 96,202)( 97,201)( 98,200)( 99,199)(100,198)(101,197)(102,196)(103,195)
(104,194)(105,193)(106,192)(107,191)(108,190)(109,189)(110,188)(111,187)
(112,186)(113,185)(114,184)(115,183)(116,182)(117,181)(118,180);
poly := sub<Sym(236)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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