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# Polytope of Type {4,48}

Atlas Canonical Name : {4,48}*768d
if this polytope has a name.
Group : SmallGroup(768,1088573)
Rank : 3
Schlafli Type : {4,48}
Number of vertices, edges, etc : 8, 192, 96
Order of s0s1s2 : 48
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,24}*384c
4-fold quotients : {4,24}*192c, {4,24}*192d, {4,12}*192b
8-fold quotients : {2,24}*96, {4,12}*96b, {4,12}*96c, {4,6}*96
16-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
24-fold quotients : {2,8}*32
32-fold quotients : {4,3}*24, {2,6}*24
48-fold quotients : {2,4}*16
64-fold quotients : {2,3}*12
96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  1,  4)(  2,  3)(  5,  8)(  6,  7)(  9, 12)( 10, 11)( 13, 16)( 14, 15)
( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)
( 33, 36)( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)
( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)
( 65, 68)( 66, 67)( 69, 72)( 70, 71)( 73, 76)( 74, 75)( 77, 80)( 78, 79)
( 81, 84)( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)
( 97,112)( 98,111)( 99,110)(100,109)(101,116)(102,115)(103,114)(104,113)
(105,120)(106,119)(107,118)(108,117)(121,136)(122,135)(123,134)(124,133)
(125,140)(126,139)(127,138)(128,137)(129,144)(130,143)(131,142)(132,141)
(145,160)(146,159)(147,158)(148,157)(149,164)(150,163)(151,162)(152,161)
(153,168)(154,167)(155,166)(156,165)(169,184)(170,183)(171,182)(172,181)
(173,188)(174,187)(175,186)(176,185)(177,192)(178,191)(179,190)(180,189);;
s1 := (  1,145)(  2,146)(  3,148)(  4,147)(  5,153)(  6,154)(  7,156)(  8,155)
(  9,149)( 10,150)( 11,152)( 12,151)( 13,157)( 14,158)( 15,160)( 16,159)
( 17,165)( 18,166)( 19,168)( 20,167)( 21,161)( 22,162)( 23,164)( 24,163)
( 25,181)( 26,182)( 27,184)( 28,183)( 29,189)( 30,190)( 31,192)( 32,191)
( 33,185)( 34,186)( 35,188)( 36,187)( 37,169)( 38,170)( 39,172)( 40,171)
( 41,177)( 42,178)( 43,180)( 44,179)( 45,173)( 46,174)( 47,176)( 48,175)
( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,105)( 54,106)( 55,108)( 56,107)
( 57,101)( 58,102)( 59,104)( 60,103)( 61,109)( 62,110)( 63,112)( 64,111)
( 65,117)( 66,118)( 67,120)( 68,119)( 69,113)( 70,114)( 71,116)( 72,115)
( 73,133)( 74,134)( 75,136)( 76,135)( 77,141)( 78,142)( 79,144)( 80,143)
( 81,137)( 82,138)( 83,140)( 84,139)( 85,121)( 86,122)( 87,124)( 88,123)
( 89,129)( 90,130)( 91,132)( 92,131)( 93,125)( 94,126)( 95,128)( 96,127);;
s2 := (  1,  9)(  2, 11)(  3, 10)(  4, 12)(  6,  7)( 13, 21)( 14, 23)( 15, 22)
( 16, 24)( 18, 19)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 41)( 30, 43)
( 31, 42)( 32, 44)( 33, 37)( 34, 39)( 35, 38)( 36, 40)( 49, 81)( 50, 83)
( 51, 82)( 52, 84)( 53, 77)( 54, 79)( 55, 78)( 56, 80)( 57, 73)( 58, 75)
( 59, 74)( 60, 76)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 65, 89)( 66, 91)
( 67, 90)( 68, 92)( 69, 85)( 70, 87)( 71, 86)( 72, 88)( 97,153)( 98,155)
( 99,154)(100,156)(101,149)(102,151)(103,150)(104,152)(105,145)(106,147)
(107,146)(108,148)(109,165)(110,167)(111,166)(112,168)(113,161)(114,163)
(115,162)(116,164)(117,157)(118,159)(119,158)(120,160)(121,189)(122,191)
(123,190)(124,192)(125,185)(126,187)(127,186)(128,188)(129,181)(130,183)
(131,182)(132,184)(133,177)(134,179)(135,178)(136,180)(137,173)(138,175)
(139,174)(140,176)(141,169)(142,171)(143,170)(144,172);;
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1,
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*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope