Polytope of Type {48,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240711)
Rank : 3
Schlafli Type : {48,6}
Number of vertices, edges, etc : 160, 480, 20
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,6}*960b
   4-fold quotients : {12,6}*480a
   8-fold quotients : {6,6}*240b
   16-fold quotients : {6,6}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope