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# Polytope of Type {144,2}

Atlas Canonical Name : {144,2}*576
if this polytope has a name.
Group : SmallGroup(576,464)
Rank : 3
Schlafli Type : {144,2}
Number of vertices, edges, etc : 144, 144, 2
Order of s0s1s2 : 144
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{144,2,2} of size 1152
{144,2,3} of size 1728
Vertex Figure Of :
{2,144,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {72,2}*288
3-fold quotients : {48,2}*192
4-fold quotients : {36,2}*144
6-fold quotients : {24,2}*96
8-fold quotients : {18,2}*72
9-fold quotients : {16,2}*64
12-fold quotients : {12,2}*48
16-fold quotients : {9,2}*36
18-fold quotients : {8,2}*32
24-fold quotients : {6,2}*24
36-fold quotients : {4,2}*16
48-fold quotients : {3,2}*12
72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {144,4}*1152a, {288,2}*1152
3-fold covers : {432,2}*1728, {144,6}*1728a, {144,6}*1728b
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);;
s2 := (145,146);;
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, s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(146)!(  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(146)!(  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);
s2 := Sym(146)!(145,146);
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*s2*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope