Part of the Atlas of Small Regular Polytopes

Polytope of Type {36,10}

Atlas Canonical Name {36,10}*1800

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Overview

Group
SmallGroup(1800,292)
Rank
3
Schläfli Type
{36,10}
Vertices, edges, …
90, 450, 25
Order of s0s1s2
36
Order of s0s1s2s1
10
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Self-Petrie

Quotients maximal quotients in bold

3-fold

9-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := (  2,  3)(  4, 16)(  5, 18)(  6, 17)(  7, 31)(  8, 33)(  9, 32)( 10, 46)( 11, 48)( 12, 47)( 13, 61)( 14, 63)( 15, 62)( 20, 21)( 22, 34)( 23, 36)( 24, 35)( 25, 49)( 26, 51)( 27, 50)( 28, 64)( 29, 66)( 30, 65)( 38, 39)( 40, 52)( 41, 54)( 42, 53)( 43, 67)( 44, 69)( 45, 68)( 56, 57)( 58, 70)( 59, 72)( 60, 71)( 74, 75)( 76,152)( 77,151)( 78,153)( 79,167)( 80,166)( 81,168)( 82,182)( 83,181)( 84,183)( 85,197)( 86,196)( 87,198)( 88,212)( 89,211)( 90,213)( 91,155)( 92,154)( 93,156)( 94,170)( 95,169)( 96,171)( 97,185)( 98,184)( 99,186)(100,200)(101,199)(102,201)(103,215)(104,214)(105,216)(106,158)(107,157)(108,159)(109,173)(110,172)(111,174)(112,188)(113,187)(114,189)(115,203)(116,202)(117,204)(118,218)(119,217)(120,219)(121,161)(122,160)(123,162)(124,176)(125,175)(126,177)(127,191)(128,190)(129,192)(130,206)(131,205)(132,207)(133,221)(134,220)(135,222)(136,164)(137,163)(138,165)(139,179)(140,178)(141,180)(142,194)(143,193)(144,195)(145,209)(146,208)(147,210)(148,224)(149,223)(150,225);;
s1 := (  1, 76)(  2, 78)(  3, 77)(  4,121)(  5,123)(  6,122)(  7, 91)(  8, 93)(  9, 92)( 10,136)( 11,138)( 12,137)( 13,106)( 14,108)( 15,107)( 16, 82)( 17, 84)( 18, 83)( 19,127)( 20,129)( 21,128)( 22, 97)( 23, 99)( 24, 98)( 25,142)( 26,144)( 27,143)( 28,112)( 29,114)( 30,113)( 31, 88)( 32, 90)( 33, 89)( 34,133)( 35,135)( 36,134)( 37,103)( 38,105)( 39,104)( 40,148)( 41,150)( 42,149)( 43,118)( 44,120)( 45,119)( 46, 79)( 47, 81)( 48, 80)( 49,124)( 50,126)( 51,125)( 52, 94)( 53, 96)( 54, 95)( 55,139)( 56,141)( 57,140)( 58,109)( 59,111)( 60,110)( 61, 85)( 62, 87)( 63, 86)( 64,130)( 65,132)( 66,131)( 67,100)( 68,102)( 69,101)( 70,145)( 71,147)( 72,146)( 73,115)( 74,117)( 75,116)(151,152)(154,197)(155,196)(156,198)(157,167)(158,166)(159,168)(160,212)(161,211)(162,213)(163,182)(164,181)(165,183)(169,203)(170,202)(171,204)(172,173)(175,218)(176,217)(177,219)(178,188)(179,187)(180,189)(184,209)(185,208)(186,210)(190,224)(191,223)(192,225)(193,194)(199,200)(205,215)(206,214)(207,216)(220,221);;
s2 := (  1, 19)(  2, 20)(  3, 21)(  4, 16)(  5, 17)(  6, 18)(  7, 28)(  8, 29)(  9, 30)( 10, 25)( 11, 26)( 12, 27)( 13, 22)( 14, 23)( 15, 24)( 31, 64)( 32, 65)( 33, 66)( 34, 61)( 35, 62)( 36, 63)( 37, 73)( 38, 74)( 39, 75)( 40, 70)( 41, 71)( 42, 72)( 43, 67)( 44, 68)( 45, 69)( 46, 49)( 47, 50)( 48, 51)( 52, 58)( 53, 59)( 54, 60)( 76, 94)( 77, 95)( 78, 96)( 79, 91)( 80, 92)( 81, 93)( 82,103)( 83,104)( 84,105)( 85,100)( 86,101)( 87,102)( 88, 97)( 89, 98)( 90, 99)(106,139)(107,140)(108,141)(109,136)(110,137)(111,138)(112,148)(113,149)(114,150)(115,145)(116,146)(117,147)(118,142)(119,143)(120,144)(121,124)(122,125)(123,126)(127,133)(128,134)(129,135)(151,169)(152,170)(153,171)(154,166)(155,167)(156,168)(157,178)(158,179)(159,180)(160,175)(161,176)(162,177)(163,172)(164,173)(165,174)(181,214)(182,215)(183,216)(184,211)(185,212)(186,213)(187,223)(188,224)(189,225)(190,220)(191,221)(192,222)(193,217)(194,218)(195,219)(196,199)(197,200)(198,201)(202,208)(203,209)(204,210);;
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*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(225)!(  2,  3)(  4, 16)(  5, 18)(  6, 17)(  7, 31)(  8, 33)(  9, 32)( 10, 46)( 11, 48)( 12, 47)( 13, 61)( 14, 63)( 15, 62)( 20, 21)( 22, 34)( 23, 36)( 24, 35)( 25, 49)( 26, 51)( 27, 50)( 28, 64)( 29, 66)( 30, 65)( 38, 39)( 40, 52)( 41, 54)( 42, 53)( 43, 67)( 44, 69)( 45, 68)( 56, 57)( 58, 70)( 59, 72)( 60, 71)( 74, 75)( 76,152)( 77,151)( 78,153)( 79,167)( 80,166)( 81,168)( 82,182)( 83,181)( 84,183)( 85,197)( 86,196)( 87,198)( 88,212)( 89,211)( 90,213)( 91,155)( 92,154)( 93,156)( 94,170)( 95,169)( 96,171)( 97,185)( 98,184)( 99,186)(100,200)(101,199)(102,201)(103,215)(104,214)(105,216)(106,158)(107,157)(108,159)(109,173)(110,172)(111,174)(112,188)(113,187)(114,189)(115,203)(116,202)(117,204)(118,218)(119,217)(120,219)(121,161)(122,160)(123,162)(124,176)(125,175)(126,177)(127,191)(128,190)(129,192)(130,206)(131,205)(132,207)(133,221)(134,220)(135,222)(136,164)(137,163)(138,165)(139,179)(140,178)(141,180)(142,194)(143,193)(144,195)(145,209)(146,208)(147,210)(148,224)(149,223)(150,225);
s1 := Sym(225)!(  1, 76)(  2, 78)(  3, 77)(  4,121)(  5,123)(  6,122)(  7, 91)(  8, 93)(  9, 92)( 10,136)( 11,138)( 12,137)( 13,106)( 14,108)( 15,107)( 16, 82)( 17, 84)( 18, 83)( 19,127)( 20,129)( 21,128)( 22, 97)( 23, 99)( 24, 98)( 25,142)( 26,144)( 27,143)( 28,112)( 29,114)( 30,113)( 31, 88)( 32, 90)( 33, 89)( 34,133)( 35,135)( 36,134)( 37,103)( 38,105)( 39,104)( 40,148)( 41,150)( 42,149)( 43,118)( 44,120)( 45,119)( 46, 79)( 47, 81)( 48, 80)( 49,124)( 50,126)( 51,125)( 52, 94)( 53, 96)( 54, 95)( 55,139)( 56,141)( 57,140)( 58,109)( 59,111)( 60,110)( 61, 85)( 62, 87)( 63, 86)( 64,130)( 65,132)( 66,131)( 67,100)( 68,102)( 69,101)( 70,145)( 71,147)( 72,146)( 73,115)( 74,117)( 75,116)(151,152)(154,197)(155,196)(156,198)(157,167)(158,166)(159,168)(160,212)(161,211)(162,213)(163,182)(164,181)(165,183)(169,203)(170,202)(171,204)(172,173)(175,218)(176,217)(177,219)(178,188)(179,187)(180,189)(184,209)(185,208)(186,210)(190,224)(191,223)(192,225)(193,194)(199,200)(205,215)(206,214)(207,216)(220,221);
s2 := Sym(225)!(  1, 19)(  2, 20)(  3, 21)(  4, 16)(  5, 17)(  6, 18)(  7, 28)(  8, 29)(  9, 30)( 10, 25)( 11, 26)( 12, 27)( 13, 22)( 14, 23)( 15, 24)( 31, 64)( 32, 65)( 33, 66)( 34, 61)( 35, 62)( 36, 63)( 37, 73)( 38, 74)( 39, 75)( 40, 70)( 41, 71)( 42, 72)( 43, 67)( 44, 68)( 45, 69)( 46, 49)( 47, 50)( 48, 51)( 52, 58)( 53, 59)( 54, 60)( 76, 94)( 77, 95)( 78, 96)( 79, 91)( 80, 92)( 81, 93)( 82,103)( 83,104)( 84,105)( 85,100)( 86,101)( 87,102)( 88, 97)( 89, 98)( 90, 99)(106,139)(107,140)(108,141)(109,136)(110,137)(111,138)(112,148)(113,149)(114,150)(115,145)(116,146)(117,147)(118,142)(119,143)(120,144)(121,124)(122,125)(123,126)(127,133)(128,134)(129,135)(151,169)(152,170)(153,171)(154,166)(155,167)(156,168)(157,178)(158,179)(159,180)(160,175)(161,176)(162,177)(163,172)(164,173)(165,174)(181,214)(182,215)(183,216)(184,211)(185,212)(186,213)(187,223)(188,224)(189,225)(190,220)(191,221)(192,222)(193,217)(194,218)(195,219)(196,199)(197,200)(198,201)(202,208)(203,209)(204,210);
poly := sub<Sym(225)|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*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 >;

References

None.

to this polytope.

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