Polytope of Type {2,144}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,144}*576
if this polytope has a name.
Group : SmallGroup(576,464)
Rank : 3
Schlafli Type : {2,144}
Number of vertices, edges, etc : 2, 144, 144
Order of s₀s₁s₂ : 144
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,144,2} of size 1152
Vertex Figure Of :
   {2,2,144} of size 1152
   {3,2,144} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,72}*288
   3-fold quotients : {2,48}*192
   4-fold quotients : {2,36}*144
   6-fold quotients : {2,24}*96
   8-fold quotients : {2,18}*72
   9-fold quotients : {2,16}*64
   12-fold quotients : {2,12}*48
   16-fold quotients : {2,9}*36
   18-fold quotients : {2,8}*32
   24-fold quotients : {2,6}*24
   36-fold quotients : {2,4}*16
   48-fold quotients : {2,3}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,144}*1152a, {2,288}*1152
   3-fold covers : {2,432}*1728, {6,144}*1728a, {6,144}*1728b
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  6, 10)(  7,  9)(  8, 11)( 13, 14)( 15, 19)( 16, 18)( 17, 20)
( 21, 30)( 22, 32)( 23, 31)( 24, 37)( 25, 36)( 26, 38)( 27, 34)( 28, 33)
( 29, 35)( 39, 57)( 40, 59)( 41, 58)( 42, 64)( 43, 63)( 44, 65)( 45, 61)
( 46, 60)( 47, 62)( 48, 66)( 49, 68)( 50, 67)( 51, 73)( 52, 72)( 53, 74)
( 54, 70)( 55, 69)( 56, 71)( 75,111)( 76,113)( 77,112)( 78,118)( 79,117)
( 80,119)( 81,115)( 82,114)( 83,116)( 84,120)( 85,122)( 86,121)( 87,127)
( 88,126)( 89,128)( 90,124)( 91,123)( 92,125)( 93,138)( 94,140)( 95,139)
( 96,145)( 97,144)( 98,146)( 99,142)(100,141)(101,143)(102,129)(103,131)
(104,130)(105,136)(106,135)(107,137)(108,133)(109,132)(110,134);;
s2 := (  3, 78)(  4, 80)(  5, 79)(  6, 75)(  7, 77)(  8, 76)(  9, 82)( 10, 81)
( 11, 83)( 12, 87)( 13, 89)( 14, 88)( 15, 84)( 16, 86)( 17, 85)( 18, 91)
( 19, 90)( 20, 92)( 21,105)( 22,107)( 23,106)( 24,102)( 25,104)( 26,103)
( 27,109)( 28,108)( 29,110)( 30, 96)( 31, 98)( 32, 97)( 33, 93)( 34, 95)
( 35, 94)( 36,100)( 37, 99)( 38,101)( 39,132)( 40,134)( 41,133)( 42,129)
( 43,131)( 44,130)( 45,136)( 46,135)( 47,137)( 48,141)( 49,143)( 50,142)
( 51,138)( 52,140)( 53,139)( 54,145)( 55,144)( 56,146)( 57,114)( 58,116)
( 59,115)( 60,111)( 61,113)( 62,112)( 63,118)( 64,117)( 65,119)( 66,123)
( 67,125)( 68,124)( 69,120)( 70,122)( 71,121)( 72,127)( 73,126)( 74,128);;
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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(146)!(1,2);
s1 := Sym(146)!(  4,  5)(  6, 10)(  7,  9)(  8, 11)( 13, 14)( 15, 19)( 16, 18)
( 17, 20)( 21, 30)( 22, 32)( 23, 31)( 24, 37)( 25, 36)( 26, 38)( 27, 34)
( 28, 33)( 29, 35)( 39, 57)( 40, 59)( 41, 58)( 42, 64)( 43, 63)( 44, 65)
( 45, 61)( 46, 60)( 47, 62)( 48, 66)( 49, 68)( 50, 67)( 51, 73)( 52, 72)
( 53, 74)( 54, 70)( 55, 69)( 56, 71)( 75,111)( 76,113)( 77,112)( 78,118)
( 79,117)( 80,119)( 81,115)( 82,114)( 83,116)( 84,120)( 85,122)( 86,121)
( 87,127)( 88,126)( 89,128)( 90,124)( 91,123)( 92,125)( 93,138)( 94,140)
( 95,139)( 96,145)( 97,144)( 98,146)( 99,142)(100,141)(101,143)(102,129)
(103,131)(104,130)(105,136)(106,135)(107,137)(108,133)(109,132)(110,134);
s2 := Sym(146)!(  3, 78)(  4, 80)(  5, 79)(  6, 75)(  7, 77)(  8, 76)(  9, 82)
( 10, 81)( 11, 83)( 12, 87)( 13, 89)( 14, 88)( 15, 84)( 16, 86)( 17, 85)
( 18, 91)( 19, 90)( 20, 92)( 21,105)( 22,107)( 23,106)( 24,102)( 25,104)
( 26,103)( 27,109)( 28,108)( 29,110)( 30, 96)( 31, 98)( 32, 97)( 33, 93)
( 34, 95)( 35, 94)( 36,100)( 37, 99)( 38,101)( 39,132)( 40,134)( 41,133)
( 42,129)( 43,131)( 44,130)( 45,136)( 46,135)( 47,137)( 48,141)( 49,143)
( 50,142)( 51,138)( 52,140)( 53,139)( 54,145)( 55,144)( 56,146)( 57,114)
( 58,116)( 59,115)( 60,111)( 61,113)( 62,112)( 63,118)( 64,117)( 65,119)
( 66,123)( 67,125)( 68,124)( 69,120)( 70,122)( 71,121)( 72,127)( 73,126)
( 74,128);
poly := sub<Sym(146)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope