Polytope of Type {6,48}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope