Polytope of Type {4,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,4}*768b
if this polytope has a name.
Group : SmallGroup(768,1087581)
Rank : 4
Schlafli Type : {4,6,4}
Number of vertices, edges, etc : 16, 48, 48, 4
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
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 : {4,6,2}*384a
   4-fold quotients : {4,6,4}*192c
   8-fold quotients : {4,6,2}*96c
   16-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1, 15)(  2, 16)(  3, 13)(  4, 14)(  5, 11)(  6, 12)(  7,  9)(  8, 10)
( 17, 31)( 18, 32)( 19, 29)( 20, 30)( 21, 27)( 22, 28)( 23, 25)( 24, 26)
( 33, 47)( 34, 48)( 35, 45)( 36, 46)( 37, 43)( 38, 44)( 39, 41)( 40, 42)
( 49, 63)( 50, 64)( 51, 61)( 52, 62)( 53, 59)( 54, 60)( 55, 57)( 56, 58)
( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 75)( 70, 76)( 71, 73)( 72, 74)
( 81, 95)( 82, 96)( 83, 93)( 84, 94)( 85, 91)( 86, 92)( 87, 89)( 88, 90)
( 97,111)( 98,112)( 99,109)(100,110)(101,107)(102,108)(103,105)(104,106)
(113,127)(114,128)(115,125)(116,126)(117,123)(118,124)(119,121)(120,122)
(129,143)(130,144)(131,141)(132,142)(133,139)(134,140)(135,137)(136,138)
(145,159)(146,160)(147,157)(148,158)(149,155)(150,156)(151,153)(152,154)
(161,175)(162,176)(163,173)(164,174)(165,171)(166,172)(167,169)(168,170)
(177,191)(178,192)(179,189)(180,190)(181,187)(182,188)(183,185)(184,186);;
s1 := (  3,  4)(  7,  8)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)( 55, 56)
( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)( 68, 83)
( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 93)( 74, 94)( 75, 96)( 76, 95)
( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 99,100)(103,104)(105,109)(106,110)
(107,112)(108,111)(113,129)(114,130)(115,132)(116,131)(117,133)(118,134)
(119,136)(120,135)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)
(127,140)(128,139)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)
(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)
(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187);;
s2 := (  1,129)(  2,131)(  3,130)(  4,132)(  5,139)(  6,137)(  7,140)(  8,138)
(  9,134)( 10,136)( 11,133)( 12,135)( 13,144)( 14,142)( 15,143)( 16,141)
( 17,113)( 18,115)( 19,114)( 20,116)( 21,123)( 22,121)( 23,124)( 24,122)
( 25,118)( 26,120)( 27,117)( 28,119)( 29,128)( 30,126)( 31,127)( 32,125)
( 33, 97)( 34, 99)( 35, 98)( 36,100)( 37,107)( 38,105)( 39,108)( 40,106)
( 41,102)( 42,104)( 43,101)( 44,103)( 45,112)( 46,110)( 47,111)( 48,109)
( 49,177)( 50,179)( 51,178)( 52,180)( 53,187)( 54,185)( 55,188)( 56,186)
( 57,182)( 58,184)( 59,181)( 60,183)( 61,192)( 62,190)( 63,191)( 64,189)
( 65,161)( 66,163)( 67,162)( 68,164)( 69,171)( 70,169)( 71,172)( 72,170)
( 73,166)( 74,168)( 75,165)( 76,167)( 77,176)( 78,174)( 79,175)( 80,173)
( 81,145)( 82,147)( 83,146)( 84,148)( 85,155)( 86,153)( 87,156)( 88,154)
( 89,150)( 90,152)( 91,149)( 92,151)( 93,160)( 94,158)( 95,159)( 96,157);;
s3 := ( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)
(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)(112,160)
(113,161)(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)(120,168)
(121,169)(122,170)(123,171)(124,172)(125,173)(126,174)(127,175)(128,176)
(129,177)(130,178)(131,179)(132,180)(133,181)(134,182)(135,183)(136,184)
(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(192)!(  1, 15)(  2, 16)(  3, 13)(  4, 14)(  5, 11)(  6, 12)(  7,  9)
(  8, 10)( 17, 31)( 18, 32)( 19, 29)( 20, 30)( 21, 27)( 22, 28)( 23, 25)
( 24, 26)( 33, 47)( 34, 48)( 35, 45)( 36, 46)( 37, 43)( 38, 44)( 39, 41)
( 40, 42)( 49, 63)( 50, 64)( 51, 61)( 52, 62)( 53, 59)( 54, 60)( 55, 57)
( 56, 58)( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 75)( 70, 76)( 71, 73)
( 72, 74)( 81, 95)( 82, 96)( 83, 93)( 84, 94)( 85, 91)( 86, 92)( 87, 89)
( 88, 90)( 97,111)( 98,112)( 99,109)(100,110)(101,107)(102,108)(103,105)
(104,106)(113,127)(114,128)(115,125)(116,126)(117,123)(118,124)(119,121)
(120,122)(129,143)(130,144)(131,141)(132,142)(133,139)(134,140)(135,137)
(136,138)(145,159)(146,160)(147,157)(148,158)(149,155)(150,156)(151,153)
(152,154)(161,175)(162,176)(163,173)(164,174)(165,171)(166,172)(167,169)
(168,170)(177,191)(178,192)(179,189)(180,190)(181,187)(182,188)(183,185)
(184,186);
s1 := Sym(192)!(  3,  4)(  7,  8)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)
( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)
( 55, 56)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)
( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 93)( 74, 94)( 75, 96)
( 76, 95)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 99,100)(103,104)(105,109)
(106,110)(107,112)(108,111)(113,129)(114,130)(115,132)(116,131)(117,133)
(118,134)(119,136)(120,135)(121,141)(122,142)(123,144)(124,143)(125,137)
(126,138)(127,140)(128,139)(147,148)(151,152)(153,157)(154,158)(155,160)
(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)
(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)
(176,187);
s2 := Sym(192)!(  1,129)(  2,131)(  3,130)(  4,132)(  5,139)(  6,137)(  7,140)
(  8,138)(  9,134)( 10,136)( 11,133)( 12,135)( 13,144)( 14,142)( 15,143)
( 16,141)( 17,113)( 18,115)( 19,114)( 20,116)( 21,123)( 22,121)( 23,124)
( 24,122)( 25,118)( 26,120)( 27,117)( 28,119)( 29,128)( 30,126)( 31,127)
( 32,125)( 33, 97)( 34, 99)( 35, 98)( 36,100)( 37,107)( 38,105)( 39,108)
( 40,106)( 41,102)( 42,104)( 43,101)( 44,103)( 45,112)( 46,110)( 47,111)
( 48,109)( 49,177)( 50,179)( 51,178)( 52,180)( 53,187)( 54,185)( 55,188)
( 56,186)( 57,182)( 58,184)( 59,181)( 60,183)( 61,192)( 62,190)( 63,191)
( 64,189)( 65,161)( 66,163)( 67,162)( 68,164)( 69,171)( 70,169)( 71,172)
( 72,170)( 73,166)( 74,168)( 75,165)( 76,167)( 77,176)( 78,174)( 79,175)
( 80,173)( 81,145)( 82,147)( 83,146)( 84,148)( 85,155)( 86,153)( 87,156)
( 88,154)( 89,150)( 90,152)( 91,149)( 92,151)( 93,160)( 94,158)( 95,159)
( 96,157);
s3 := Sym(192)!( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)
(104,152)(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)
(112,160)(113,161)(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)
(120,168)(121,169)(122,170)(123,171)(124,172)(125,173)(126,174)(127,175)
(128,176)(129,177)(130,178)(131,179)(132,180)(133,181)(134,182)(135,183)
(136,184)(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)
(144,192);
poly := sub<Sym(192)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 >;

References : None.
to this polytope