Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,36}

Atlas Canonical Name {10,36}*1800

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Overview

Group
SmallGroup(1800,292)
Rank
3
Schläfli Type
{10,36}
Vertices, edges, …
25, 450, 90
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

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

References

None.

to this polytope.

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