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# Polytope of Type {4,48}

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