Part of the Atlas of Small Regular Polytopes

Polytope of Type {36,12,2}

Atlas Canonical Name {36,12,2}*1728b

Overview

Group
SmallGroup(1728,16615)
Rank
4
Schläfli Type
{36,12,2}
Vertices, edges, …
36, 216, 12, 2
Order of s0s1s2s3
36
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

9-fold

12-fold

18-fold

24-fold

27-fold

36-fold

54-fold

72-fold

108-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (  2,  3)(  4,  7)(  5,  9)(  6,  8)( 10, 21)( 11, 20)( 12, 19)( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 75)( 65, 74)( 66, 73)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 91,102)( 92,101)( 93,100)( 94,108)( 95,107)( 96,106)( 97,105)( 98,104)( 99,103)(109,190)(110,192)(111,191)(112,196)(113,198)(114,197)(115,193)(116,195)(117,194)(118,210)(119,209)(120,208)(121,216)(122,215)(123,214)(124,213)(125,212)(126,211)(127,201)(128,200)(129,199)(130,207)(131,206)(132,205)(133,204)(134,203)(135,202)(136,163)(137,165)(138,164)(139,169)(140,171)(141,170)(142,166)(143,168)(144,167)(145,183)(146,182)(147,181)(148,189)(149,188)(150,187)(151,186)(152,185)(153,184)(154,174)(155,173)(156,172)(157,180)(158,179)(159,178)(160,177)(161,176)(162,175);;
s1 := (  1,121)(  2,123)(  3,122)(  4,118)(  5,120)(  6,119)(  7,124)(  8,126)(  9,125)( 10,112)( 11,114)( 12,113)( 13,109)( 14,111)( 15,110)( 16,115)( 17,117)( 18,116)( 19,132)( 20,131)( 21,130)( 22,129)( 23,128)( 24,127)( 25,135)( 26,134)( 27,133)( 28,148)( 29,150)( 30,149)( 31,145)( 32,147)( 33,146)( 34,151)( 35,153)( 36,152)( 37,139)( 38,141)( 39,140)( 40,136)( 41,138)( 42,137)( 43,142)( 44,144)( 45,143)( 46,159)( 47,158)( 48,157)( 49,156)( 50,155)( 51,154)( 52,162)( 53,161)( 54,160)( 55,175)( 56,177)( 57,176)( 58,172)( 59,174)( 60,173)( 61,178)( 62,180)( 63,179)( 64,166)( 65,168)( 66,167)( 67,163)( 68,165)( 69,164)( 70,169)( 71,171)( 72,170)( 73,186)( 74,185)( 75,184)( 76,183)( 77,182)( 78,181)( 79,189)( 80,188)( 81,187)( 82,202)( 83,204)( 84,203)( 85,199)( 86,201)( 87,200)( 88,205)( 89,207)( 90,206)( 91,193)( 92,195)( 93,194)( 94,190)( 95,192)( 96,191)( 97,196)( 98,198)( 99,197)(100,213)(101,212)(102,211)(103,210)(104,209)(105,208)(106,216)(107,215)(108,214);;
s2 := (  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)(111,138)(112,142)(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)(119,146)(120,147)(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)(127,154)(128,155)(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)(135,159)(163,190)(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)(171,195)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)(179,203)(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)(187,211)(188,212)(189,213);;
s3 := (217,218);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(218)!(  2,  3)(  4,  7)(  5,  9)(  6,  8)( 10, 21)( 11, 20)( 12, 19)( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 75)( 65, 74)( 66, 73)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 91,102)( 92,101)( 93,100)( 94,108)( 95,107)( 96,106)( 97,105)( 98,104)( 99,103)(109,190)(110,192)(111,191)(112,196)(113,198)(114,197)(115,193)(116,195)(117,194)(118,210)(119,209)(120,208)(121,216)(122,215)(123,214)(124,213)(125,212)(126,211)(127,201)(128,200)(129,199)(130,207)(131,206)(132,205)(133,204)(134,203)(135,202)(136,163)(137,165)(138,164)(139,169)(140,171)(141,170)(142,166)(143,168)(144,167)(145,183)(146,182)(147,181)(148,189)(149,188)(150,187)(151,186)(152,185)(153,184)(154,174)(155,173)(156,172)(157,180)(158,179)(159,178)(160,177)(161,176)(162,175);
s1 := Sym(218)!(  1,121)(  2,123)(  3,122)(  4,118)(  5,120)(  6,119)(  7,124)(  8,126)(  9,125)( 10,112)( 11,114)( 12,113)( 13,109)( 14,111)( 15,110)( 16,115)( 17,117)( 18,116)( 19,132)( 20,131)( 21,130)( 22,129)( 23,128)( 24,127)( 25,135)( 26,134)( 27,133)( 28,148)( 29,150)( 30,149)( 31,145)( 32,147)( 33,146)( 34,151)( 35,153)( 36,152)( 37,139)( 38,141)( 39,140)( 40,136)( 41,138)( 42,137)( 43,142)( 44,144)( 45,143)( 46,159)( 47,158)( 48,157)( 49,156)( 50,155)( 51,154)( 52,162)( 53,161)( 54,160)( 55,175)( 56,177)( 57,176)( 58,172)( 59,174)( 60,173)( 61,178)( 62,180)( 63,179)( 64,166)( 65,168)( 66,167)( 67,163)( 68,165)( 69,164)( 70,169)( 71,171)( 72,170)( 73,186)( 74,185)( 75,184)( 76,183)( 77,182)( 78,181)( 79,189)( 80,188)( 81,187)( 82,202)( 83,204)( 84,203)( 85,199)( 86,201)( 87,200)( 88,205)( 89,207)( 90,206)( 91,193)( 92,195)( 93,194)( 94,190)( 95,192)( 96,191)( 97,196)( 98,198)( 99,197)(100,213)(101,212)(102,211)(103,210)(104,209)(105,208)(106,216)(107,215)(108,214);
s2 := Sym(218)!(  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)(111,138)(112,142)(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)(119,146)(120,147)(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)(127,154)(128,155)(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)(135,159)(163,190)(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)(171,195)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)(179,203)(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)(187,211)(188,212)(189,213);
s3 := Sym(218)!(217,218);
poly := sub<Sym(218)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;