Part of the Atlas of Small Regular Polytopes

Polytope of Type {258}

Atlas Canonical Name {258}*516

Overview

Group
SmallGroup(516,14)
Rank
2
Schläfli Type
{258}
Vertices, edges, …
258, 258
Order of s0s1
258
Also known as
258-gon, {258}. if this polytope has another name.

Special Properties

  • Universal
  • Spherical
  • Locally Spherical
  • Orientable
  • Self-Dual

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

43-fold

86-fold

129-fold

Covers minimal covers in bold

2-fold

3-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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