Polytope of Type {226}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {226}*452
Also Known As : 226-gon, {226}. if this polytope has another name.
Group : SmallGroup(452,4)
Rank : 2
Schlafli Type : {226}
Number of vertices, edges, etc : 226, 226
Order of s0s1 : 226
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{226,2} of size 904
{226,4} of size 1808
Vertex Figure Of :
{2,226} of size 904
{4,226} of size 1808
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {113}*226
113-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {452}*904
3-fold covers : {678}*1356
4-fold covers : {904}*1808
Permutation Representation (GAP) :
s0 := ( 2,113)( 3,112)( 4,111)( 5,110)( 6,109)( 7,108)( 8,107)( 9,106)
( 10,105)( 11,104)( 12,103)( 13,102)( 14,101)( 15,100)( 16, 99)( 17, 98)
( 18, 97)( 19, 96)( 20, 95)( 21, 94)( 22, 93)( 23, 92)( 24, 91)( 25, 90)
( 26, 89)( 27, 88)( 28, 87)( 29, 86)( 30, 85)( 31, 84)( 32, 83)( 33, 82)
( 34, 81)( 35, 80)( 36, 79)( 37, 78)( 38, 77)( 39, 76)( 40, 75)( 41, 74)
( 42, 73)( 43, 72)( 44, 71)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)
( 50, 65)( 51, 64)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)( 57, 58)
(115,226)(116,225)(117,224)(118,223)(119,222)(120,221)(121,220)(122,219)
(123,218)(124,217)(125,216)(126,215)(127,214)(128,213)(129,212)(130,211)
(131,210)(132,209)(133,208)(134,207)(135,206)(136,205)(137,204)(138,203)
(139,202)(140,201)(141,200)(142,199)(143,198)(144,197)(145,196)(146,195)
(147,194)(148,193)(149,192)(150,191)(151,190)(152,189)(153,188)(154,187)
(155,186)(156,185)(157,184)(158,183)(159,182)(160,181)(161,180)(162,179)
(163,178)(164,177)(165,176)(166,175)(167,174)(168,173)(169,172)(170,171);;
s1 := ( 1,115)( 2,114)( 3,226)( 4,225)( 5,224)( 6,223)( 7,222)( 8,221)
( 9,220)( 10,219)( 11,218)( 12,217)( 13,216)( 14,215)( 15,214)( 16,213)
( 17,212)( 18,211)( 19,210)( 20,209)( 21,208)( 22,207)( 23,206)( 24,205)
( 25,204)( 26,203)( 27,202)( 28,201)( 29,200)( 30,199)( 31,198)( 32,197)
( 33,196)( 34,195)( 35,194)( 36,193)( 37,192)( 38,191)( 39,190)( 40,189)
( 41,188)( 42,187)( 43,186)( 44,185)( 45,184)( 46,183)( 47,182)( 48,181)
( 49,180)( 50,179)( 51,178)( 52,177)( 53,176)( 54,175)( 55,174)( 56,173)
( 57,172)( 58,171)( 59,170)( 60,169)( 61,168)( 62,167)( 63,166)( 64,165)
( 65,164)( 66,163)( 67,162)( 68,161)( 69,160)( 70,159)( 71,158)( 72,157)
( 73,156)( 74,155)( 75,154)( 76,153)( 77,152)( 78,151)( 79,150)( 80,149)
( 81,148)( 82,147)( 83,146)( 84,145)( 85,144)( 86,143)( 87,142)( 88,141)
( 89,140)( 90,139)( 91,138)( 92,137)( 93,136)( 94,135)( 95,134)( 96,133)
( 97,132)( 98,131)( 99,130)(100,129)(101,128)(102,127)(103,126)(104,125)
(105,124)(106,123)(107,122)(108,121)(109,120)(110,119)(111,118)(112,117)
(113,116);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(226)!( 2,113)( 3,112)( 4,111)( 5,110)( 6,109)( 7,108)( 8,107)
( 9,106)( 10,105)( 11,104)( 12,103)( 13,102)( 14,101)( 15,100)( 16, 99)
( 17, 98)( 18, 97)( 19, 96)( 20, 95)( 21, 94)( 22, 93)( 23, 92)( 24, 91)
( 25, 90)( 26, 89)( 27, 88)( 28, 87)( 29, 86)( 30, 85)( 31, 84)( 32, 83)
( 33, 82)( 34, 81)( 35, 80)( 36, 79)( 37, 78)( 38, 77)( 39, 76)( 40, 75)
( 41, 74)( 42, 73)( 43, 72)( 44, 71)( 45, 70)( 46, 69)( 47, 68)( 48, 67)
( 49, 66)( 50, 65)( 51, 64)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)
( 57, 58)(115,226)(116,225)(117,224)(118,223)(119,222)(120,221)(121,220)
(122,219)(123,218)(124,217)(125,216)(126,215)(127,214)(128,213)(129,212)
(130,211)(131,210)(132,209)(133,208)(134,207)(135,206)(136,205)(137,204)
(138,203)(139,202)(140,201)(141,200)(142,199)(143,198)(144,197)(145,196)
(146,195)(147,194)(148,193)(149,192)(150,191)(151,190)(152,189)(153,188)
(154,187)(155,186)(156,185)(157,184)(158,183)(159,182)(160,181)(161,180)
(162,179)(163,178)(164,177)(165,176)(166,175)(167,174)(168,173)(169,172)
(170,171);
s1 := Sym(226)!( 1,115)( 2,114)( 3,226)( 4,225)( 5,224)( 6,223)( 7,222)
( 8,221)( 9,220)( 10,219)( 11,218)( 12,217)( 13,216)( 14,215)( 15,214)
( 16,213)( 17,212)( 18,211)( 19,210)( 20,209)( 21,208)( 22,207)( 23,206)
( 24,205)( 25,204)( 26,203)( 27,202)( 28,201)( 29,200)( 30,199)( 31,198)
( 32,197)( 33,196)( 34,195)( 35,194)( 36,193)( 37,192)( 38,191)( 39,190)
( 40,189)( 41,188)( 42,187)( 43,186)( 44,185)( 45,184)( 46,183)( 47,182)
( 48,181)( 49,180)( 50,179)( 51,178)( 52,177)( 53,176)( 54,175)( 55,174)
( 56,173)( 57,172)( 58,171)( 59,170)( 60,169)( 61,168)( 62,167)( 63,166)
( 64,165)( 65,164)( 66,163)( 67,162)( 68,161)( 69,160)( 70,159)( 71,158)
( 72,157)( 73,156)( 74,155)( 75,154)( 76,153)( 77,152)( 78,151)( 79,150)
( 80,149)( 81,148)( 82,147)( 83,146)( 84,145)( 85,144)( 86,143)( 87,142)
( 88,141)( 89,140)( 90,139)( 91,138)( 92,137)( 93,136)( 94,135)( 95,134)
( 96,133)( 97,132)( 98,131)( 99,130)(100,129)(101,128)(102,127)(103,126)
(104,125)(105,124)(106,123)(107,122)(108,121)(109,120)(110,119)(111,118)
(112,117)(113,116);
poly := sub<Sym(226)|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 >;
References : None.
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