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# Polytope of Type {6,48}

Atlas Canonical Name : {6,48}*576a
Also Known As : {6,48|2}. if this polytope has another name.
Group : SmallGroup(576,2112)
Rank : 3
Schlafli Type : {6,48}
Number of vertices, edges, etc : 6, 144, 48
Order of s0s1s2 : 48
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,48,2} of size 1152
Vertex Figure Of :
{2,6,48} of size 1152
{3,6,48} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,24}*288a
3-fold quotients : {2,48}*192, {6,16}*192
4-fold quotients : {6,12}*144a
6-fold quotients : {2,24}*96, {6,8}*96
8-fold quotients : {6,6}*72a
9-fold quotients : {2,16}*64
12-fold quotients : {2,12}*48, {6,4}*48a
18-fold quotients : {2,8}*32
24-fold quotients : {2,6}*24, {6,2}*24
36-fold quotients : {2,4}*16
48-fold quotients : {2,3}*12, {3,2}*12
72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,48}*1152b, {6,96}*1152c
3-fold covers : {6,144}*1728a, {18,48}*1728a, {6,48}*1728b, {6,48}*1728f
Permutation Representation (GAP) :
```s0 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)
( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 65, 66)( 68, 69)( 71, 72)
( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 86, 87)( 89, 90)( 92, 93)( 95, 96)
( 98, 99)(101,102)(104,105)(107,108)(110,111)(113,114)(116,117)(119,120)
(122,123)(125,126)(128,129)(131,132)(134,135)(137,138)(140,141)(143,144);;
s1 := (  1,  2)(  4,  8)(  5,  7)(  6,  9)( 10, 11)( 13, 17)( 14, 16)( 15, 18)
( 19, 29)( 20, 28)( 21, 30)( 22, 35)( 23, 34)( 24, 36)( 25, 32)( 26, 31)
( 27, 33)( 37, 56)( 38, 55)( 39, 57)( 40, 62)( 41, 61)( 42, 63)( 43, 59)
( 44, 58)( 45, 60)( 46, 65)( 47, 64)( 48, 66)( 49, 71)( 50, 70)( 51, 72)
( 52, 68)( 53, 67)( 54, 69)( 73,110)( 74,109)( 75,111)( 76,116)( 77,115)
( 78,117)( 79,113)( 80,112)( 81,114)( 82,119)( 83,118)( 84,120)( 85,125)
( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,137)( 92,136)( 93,138)
( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,128)(101,127)
(102,129)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132);;
s2 := (  1, 76)(  2, 77)(  3, 78)(  4, 73)(  5, 74)(  6, 75)(  7, 79)(  8, 80)
(  9, 81)( 10, 85)( 11, 86)( 12, 87)( 13, 82)( 14, 83)( 15, 84)( 16, 88)
( 17, 89)( 18, 90)( 19,103)( 20,104)( 21,105)( 22,100)( 23,101)( 24,102)
( 25,106)( 26,107)( 27,108)( 28, 94)( 29, 95)( 30, 96)( 31, 91)( 32, 92)
( 33, 93)( 34, 97)( 35, 98)( 36, 99)( 37,130)( 38,131)( 39,132)( 40,127)
( 41,128)( 42,129)( 43,133)( 44,134)( 45,135)( 46,139)( 47,140)( 48,141)
( 49,136)( 50,137)( 51,138)( 52,142)( 53,143)( 54,144)( 55,112)( 56,113)
( 57,114)( 58,109)( 59,110)( 60,111)( 61,115)( 62,116)( 63,117)( 64,121)
( 65,122)( 66,123)( 67,118)( 68,119)( 69,120)( 70,124)( 71,125)( 72,126);;
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*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(144)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)
( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)
( 47, 48)( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 65, 66)( 68, 69)
( 71, 72)( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 86, 87)( 89, 90)( 92, 93)
( 95, 96)( 98, 99)(101,102)(104,105)(107,108)(110,111)(113,114)(116,117)
(119,120)(122,123)(125,126)(128,129)(131,132)(134,135)(137,138)(140,141)
(143,144);
s1 := Sym(144)!(  1,  2)(  4,  8)(  5,  7)(  6,  9)( 10, 11)( 13, 17)( 14, 16)
( 15, 18)( 19, 29)( 20, 28)( 21, 30)( 22, 35)( 23, 34)( 24, 36)( 25, 32)
( 26, 31)( 27, 33)( 37, 56)( 38, 55)( 39, 57)( 40, 62)( 41, 61)( 42, 63)
( 43, 59)( 44, 58)( 45, 60)( 46, 65)( 47, 64)( 48, 66)( 49, 71)( 50, 70)
( 51, 72)( 52, 68)( 53, 67)( 54, 69)( 73,110)( 74,109)( 75,111)( 76,116)
( 77,115)( 78,117)( 79,113)( 80,112)( 81,114)( 82,119)( 83,118)( 84,120)
( 85,125)( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,137)( 92,136)
( 93,138)( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,128)
(101,127)(102,129)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132);
s2 := Sym(144)!(  1, 76)(  2, 77)(  3, 78)(  4, 73)(  5, 74)(  6, 75)(  7, 79)
(  8, 80)(  9, 81)( 10, 85)( 11, 86)( 12, 87)( 13, 82)( 14, 83)( 15, 84)
( 16, 88)( 17, 89)( 18, 90)( 19,103)( 20,104)( 21,105)( 22,100)( 23,101)
( 24,102)( 25,106)( 26,107)( 27,108)( 28, 94)( 29, 95)( 30, 96)( 31, 91)
( 32, 92)( 33, 93)( 34, 97)( 35, 98)( 36, 99)( 37,130)( 38,131)( 39,132)
( 40,127)( 41,128)( 42,129)( 43,133)( 44,134)( 45,135)( 46,139)( 47,140)
( 48,141)( 49,136)( 50,137)( 51,138)( 52,142)( 53,143)( 54,144)( 55,112)
( 56,113)( 57,114)( 58,109)( 59,110)( 60,111)( 61,115)( 62,116)( 63,117)
( 64,121)( 65,122)( 66,123)( 67,118)( 68,119)( 69,120)( 70,124)( 71,125)
( 72,126);
poly := sub<Sym(144)|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*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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