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# Polytope of Type {48,4}

Atlas Canonical Name : {48,4}*384c
if this polytope has a name.
Group : SmallGroup(384,5611)
Rank : 3
Schlafli Type : {48,4}
Number of vertices, edges, etc : 48, 96, 4
Order of s0s1s2 : 48
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{48,4,2} of size 768
Vertex Figure Of :
{2,48,4} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {24,4}*192c
4-fold quotients : {12,4}*96b
8-fold quotients : {6,4}*48c
16-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {96,4}*768c, {96,4}*768d, {48,4}*768c
3-fold covers : {144,4}*1152c
5-fold covers : {240,4}*1920c
Permutation Representation (GAP) :
```s0 := (  2,  3)(  5,  9)(  6, 11)(  7, 10)(  8, 12)( 14, 15)( 17, 21)( 18, 23)
( 19, 22)( 20, 24)( 25, 37)( 26, 39)( 27, 38)( 28, 40)( 29, 45)( 30, 47)
( 31, 46)( 32, 48)( 33, 41)( 34, 43)( 35, 42)( 36, 44)( 49, 73)( 50, 75)
( 51, 74)( 52, 76)( 53, 81)( 54, 83)( 55, 82)( 56, 84)( 57, 77)( 58, 79)
( 59, 78)( 60, 80)( 61, 85)( 62, 87)( 63, 86)( 64, 88)( 65, 93)( 66, 95)
( 67, 94)( 68, 96)( 69, 89)( 70, 91)( 71, 90)( 72, 92)( 97,145)( 98,147)
( 99,146)(100,148)(101,153)(102,155)(103,154)(104,156)(105,149)(106,151)
(107,150)(108,152)(109,157)(110,159)(111,158)(112,160)(113,165)(114,167)
(115,166)(116,168)(117,161)(118,163)(119,162)(120,164)(121,181)(122,183)
(123,182)(124,184)(125,189)(126,191)(127,190)(128,192)(129,185)(130,187)
(131,186)(132,188)(133,169)(134,171)(135,170)(136,172)(137,177)(138,179)
(139,178)(140,180)(141,173)(142,175)(143,174)(144,176);;
s1 := (  1,101)(  2,102)(  3,104)(  4,103)(  5, 97)(  6, 98)(  7,100)(  8, 99)
(  9,105)( 10,106)( 11,108)( 12,107)( 13,113)( 14,114)( 15,116)( 16,115)
( 17,109)( 18,110)( 19,112)( 20,111)( 21,117)( 22,118)( 23,120)( 24,119)
( 25,137)( 26,138)( 27,140)( 28,139)( 29,133)( 30,134)( 31,136)( 32,135)
( 33,141)( 34,142)( 35,144)( 36,143)( 37,125)( 38,126)( 39,128)( 40,127)
( 41,121)( 42,122)( 43,124)( 44,123)( 45,129)( 46,130)( 47,132)( 48,131)
( 49,173)( 50,174)( 51,176)( 52,175)( 53,169)( 54,170)( 55,172)( 56,171)
( 57,177)( 58,178)( 59,180)( 60,179)( 61,185)( 62,186)( 63,188)( 64,187)
( 65,181)( 66,182)( 67,184)( 68,183)( 69,189)( 70,190)( 71,192)( 72,191)
( 73,149)( 74,150)( 75,152)( 76,151)( 77,145)( 78,146)( 79,148)( 80,147)
( 81,153)( 82,154)( 83,156)( 84,155)( 85,161)( 86,162)( 87,164)( 88,163)
( 89,157)( 90,158)( 91,160)( 92,159)( 93,165)( 94,166)( 95,168)( 96,167);;
s2 := (  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)
( 97,100)( 98, 99)(101,104)(102,103)(105,108)(106,107)(109,112)(110,111)
(113,116)(114,115)(117,120)(118,119)(121,124)(122,123)(125,128)(126,127)
(129,132)(130,131)(133,136)(134,135)(137,140)(138,139)(141,144)(142,143)
(145,148)(146,147)(149,152)(150,151)(153,156)(154,155)(157,160)(158,159)
(161,164)(162,163)(165,168)(166,167)(169,172)(170,171)(173,176)(174,175)
(177,180)(178,179)(181,184)(182,183)(185,188)(186,187)(189,192)(190,191);;
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*s1*s2*s1*s2,
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(192)!(  2,  3)(  5,  9)(  6, 11)(  7, 10)(  8, 12)( 14, 15)( 17, 21)
( 18, 23)( 19, 22)( 20, 24)( 25, 37)( 26, 39)( 27, 38)( 28, 40)( 29, 45)
( 30, 47)( 31, 46)( 32, 48)( 33, 41)( 34, 43)( 35, 42)( 36, 44)( 49, 73)
( 50, 75)( 51, 74)( 52, 76)( 53, 81)( 54, 83)( 55, 82)( 56, 84)( 57, 77)
( 58, 79)( 59, 78)( 60, 80)( 61, 85)( 62, 87)( 63, 86)( 64, 88)( 65, 93)
( 66, 95)( 67, 94)( 68, 96)( 69, 89)( 70, 91)( 71, 90)( 72, 92)( 97,145)
( 98,147)( 99,146)(100,148)(101,153)(102,155)(103,154)(104,156)(105,149)
(106,151)(107,150)(108,152)(109,157)(110,159)(111,158)(112,160)(113,165)
(114,167)(115,166)(116,168)(117,161)(118,163)(119,162)(120,164)(121,181)
(122,183)(123,182)(124,184)(125,189)(126,191)(127,190)(128,192)(129,185)
(130,187)(131,186)(132,188)(133,169)(134,171)(135,170)(136,172)(137,177)
(138,179)(139,178)(140,180)(141,173)(142,175)(143,174)(144,176);
s1 := Sym(192)!(  1,101)(  2,102)(  3,104)(  4,103)(  5, 97)(  6, 98)(  7,100)
(  8, 99)(  9,105)( 10,106)( 11,108)( 12,107)( 13,113)( 14,114)( 15,116)
( 16,115)( 17,109)( 18,110)( 19,112)( 20,111)( 21,117)( 22,118)( 23,120)
( 24,119)( 25,137)( 26,138)( 27,140)( 28,139)( 29,133)( 30,134)( 31,136)
( 32,135)( 33,141)( 34,142)( 35,144)( 36,143)( 37,125)( 38,126)( 39,128)
( 40,127)( 41,121)( 42,122)( 43,124)( 44,123)( 45,129)( 46,130)( 47,132)
( 48,131)( 49,173)( 50,174)( 51,176)( 52,175)( 53,169)( 54,170)( 55,172)
( 56,171)( 57,177)( 58,178)( 59,180)( 60,179)( 61,185)( 62,186)( 63,188)
( 64,187)( 65,181)( 66,182)( 67,184)( 68,183)( 69,189)( 70,190)( 71,192)
( 72,191)( 73,149)( 74,150)( 75,152)( 76,151)( 77,145)( 78,146)( 79,148)
( 80,147)( 81,153)( 82,154)( 83,156)( 84,155)( 85,161)( 86,162)( 87,164)
( 88,163)( 89,157)( 90,158)( 91,160)( 92,159)( 93,165)( 94,166)( 95,168)
( 96,167);
s2 := 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)( 97,100)( 98, 99)(101,104)(102,103)(105,108)(106,107)(109,112)
(110,111)(113,116)(114,115)(117,120)(118,119)(121,124)(122,123)(125,128)
(126,127)(129,132)(130,131)(133,136)(134,135)(137,140)(138,139)(141,144)
(142,143)(145,148)(146,147)(149,152)(150,151)(153,156)(154,155)(157,160)
(158,159)(161,164)(162,163)(165,168)(166,167)(169,172)(170,171)(173,176)
(174,175)(177,180)(178,179)(181,184)(182,183)(185,188)(186,187)(189,192)
(190,191);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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