Part of the Atlas of Small Regular Polytopes

Polytope of Type {144}

Atlas Canonical Name {144}*288

Overview

Group
SmallGroup(288,6)
Rank
2
Schläfli Type
{144}
Vertices, edges, …
144, 144
Order of s0s1
144
Also known as
144-gon, {144}. if this polytope has another name.

Special Properties

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

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

9-fold

12-fold

16-fold

18-fold

24-fold

36-fold

48-fold

72-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := (  2,  3)(  4,  8)(  5,  7)(  6,  9)( 11, 12)( 13, 17)( 14, 16)( 15, 18)( 19, 28)( 20, 30)( 21, 29)( 22, 35)( 23, 34)( 24, 36)( 25, 32)( 26, 31)( 27, 33)( 37, 55)( 38, 57)( 39, 56)( 40, 62)( 41, 61)( 42, 63)( 43, 59)( 44, 58)( 45, 60)( 46, 64)( 47, 66)( 48, 65)( 49, 71)( 50, 70)( 51, 72)( 52, 68)( 53, 67)( 54, 69)( 73,109)( 74,111)( 75,110)( 76,116)( 77,115)( 78,117)( 79,113)( 80,112)( 81,114)( 82,118)( 83,120)( 84,119)( 85,125)( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,136)( 92,138)( 93,137)( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,127)(101,129)(102,128)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132);;
s1 := (  1, 76)(  2, 78)(  3, 77)(  4, 73)(  5, 75)(  6, 74)(  7, 80)(  8, 79)(  9, 81)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 89)( 17, 88)( 18, 90)( 19,103)( 20,105)( 21,104)( 22,100)( 23,102)( 24,101)( 25,107)( 26,106)( 27,108)( 28, 94)( 29, 96)( 30, 95)( 31, 91)( 32, 93)( 33, 92)( 34, 98)( 35, 97)( 36, 99)( 37,130)( 38,132)( 39,131)( 40,127)( 41,129)( 42,128)( 43,134)( 44,133)( 45,135)( 46,139)( 47,141)( 48,140)( 49,136)( 50,138)( 51,137)( 52,143)( 53,142)( 54,144)( 55,112)( 56,114)( 57,113)( 58,109)( 59,111)( 60,110)( 61,116)( 62,115)( 63,117)( 64,121)( 65,123)( 66,122)( 67,118)( 68,120)( 69,119)( 70,125)( 71,124)( 72,126);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(144)!(  2,  3)(  4,  8)(  5,  7)(  6,  9)( 11, 12)( 13, 17)( 14, 16)( 15, 18)( 19, 28)( 20, 30)( 21, 29)( 22, 35)( 23, 34)( 24, 36)( 25, 32)( 26, 31)( 27, 33)( 37, 55)( 38, 57)( 39, 56)( 40, 62)( 41, 61)( 42, 63)( 43, 59)( 44, 58)( 45, 60)( 46, 64)( 47, 66)( 48, 65)( 49, 71)( 50, 70)( 51, 72)( 52, 68)( 53, 67)( 54, 69)( 73,109)( 74,111)( 75,110)( 76,116)( 77,115)( 78,117)( 79,113)( 80,112)( 81,114)( 82,118)( 83,120)( 84,119)( 85,125)( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,136)( 92,138)( 93,137)( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,127)(101,129)(102,128)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132);
s1 := Sym(144)!(  1, 76)(  2, 78)(  3, 77)(  4, 73)(  5, 75)(  6, 74)(  7, 80)(  8, 79)(  9, 81)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 89)( 17, 88)( 18, 90)( 19,103)( 20,105)( 21,104)( 22,100)( 23,102)( 24,101)( 25,107)( 26,106)( 27,108)( 28, 94)( 29, 96)( 30, 95)( 31, 91)( 32, 93)( 33, 92)( 34, 98)( 35, 97)( 36, 99)( 37,130)( 38,132)( 39,131)( 40,127)( 41,129)( 42,128)( 43,134)( 44,133)( 45,135)( 46,139)( 47,141)( 48,140)( 49,136)( 50,138)( 51,137)( 52,143)( 53,142)( 54,144)( 55,112)( 56,114)( 57,113)( 58,109)( 59,111)( 60,110)( 61,116)( 62,115)( 63,117)( 64,121)( 65,123)( 66,122)( 67,118)( 68,120)( 69,119)( 70,125)( 71,124)( 72,126);
poly := sub<Sym(144)|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 >;

References

None.

to this polytope.