Polytope of Type {4,24,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24,4}*768j
if this polytope has a name.
Group : SmallGroup(768,1087747)
Rank : 4
Schlafli Type : {4,24,4}
Number of vertices, edges, etc : 4, 48, 48, 4
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {4,12,4}*384b
4-fold quotients : {2,12,4}*192b, {4,6,4}*192b
8-fold quotients : {2,6,4}*96c
16-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 43)( 32, 44)
( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 73, 85)( 74, 86)( 75, 87)( 76, 88)
( 77, 89)( 78, 90)( 79, 91)( 80, 92)( 81, 93)( 82, 94)( 83, 95)( 84, 96)
( 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)
(121,181)(122,182)(123,183)(124,184)(125,185)(126,186)(127,187)(128,188)
(129,189)(130,190)(131,191)(132,192)(133,169)(134,170)(135,171)(136,172)
(137,173)(138,174)(139,175)(140,176)(141,177)(142,178)(143,179)(144,180);;
s1 := ( 1,121)( 2,122)( 3,124)( 4,123)( 5,129)( 6,130)( 7,132)( 8,131)
( 9,125)( 10,126)( 11,128)( 12,127)( 13,133)( 14,134)( 15,136)( 16,135)
( 17,141)( 18,142)( 19,144)( 20,143)( 21,137)( 22,138)( 23,140)( 24,139)
( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,105)( 30,106)( 31,108)( 32,107)
( 33,101)( 34,102)( 35,104)( 36,103)( 37,109)( 38,110)( 39,112)( 40,111)
( 41,117)( 42,118)( 43,120)( 44,119)( 45,113)( 46,114)( 47,116)( 48,115)
( 49,169)( 50,170)( 51,172)( 52,171)( 53,177)( 54,178)( 55,180)( 56,179)
( 57,173)( 58,174)( 59,176)( 60,175)( 61,181)( 62,182)( 63,184)( 64,183)
( 65,189)( 66,190)( 67,192)( 68,191)( 69,185)( 70,186)( 71,188)( 72,187)
( 73,145)( 74,146)( 75,148)( 76,147)( 77,153)( 78,154)( 79,156)( 80,155)
( 81,149)( 82,150)( 83,152)( 84,151)( 85,157)( 86,158)( 87,160)( 88,159)
( 89,165)( 90,166)( 91,168)( 92,167)( 93,161)( 94,162)( 95,164)( 96,163);;
s2 := ( 1, 9)( 2, 11)( 3, 10)( 4, 12)( 6, 7)( 13, 21)( 14, 23)( 15, 22)
( 16, 24)( 18, 19)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 41)( 30, 43)
( 31, 42)( 32, 44)( 33, 37)( 34, 39)( 35, 38)( 36, 40)( 49, 69)( 50, 71)
( 51, 70)( 52, 72)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 61)( 58, 63)
( 59, 62)( 60, 64)( 73, 81)( 74, 83)( 75, 82)( 76, 84)( 78, 79)( 85, 93)
( 86, 95)( 87, 94)( 88, 96)( 90, 91)( 97,129)( 98,131)( 99,130)(100,132)
(101,125)(102,127)(103,126)(104,128)(105,121)(106,123)(107,122)(108,124)
(109,141)(110,143)(111,142)(112,144)(113,137)(114,139)(115,138)(116,140)
(117,133)(118,135)(119,134)(120,136)(145,189)(146,191)(147,190)(148,192)
(149,185)(150,187)(151,186)(152,188)(153,181)(154,183)(155,182)(156,184)
(157,177)(158,179)(159,178)(160,180)(161,173)(162,175)(163,174)(164,176)
(165,169)(166,171)(167,170)(168,172);;
s3 := ( 1, 14)( 2, 13)( 3, 16)( 4, 15)( 5, 18)( 6, 17)( 7, 20)( 8, 19)
( 9, 22)( 10, 21)( 11, 24)( 12, 23)( 25, 38)( 26, 37)( 27, 40)( 28, 39)
( 29, 42)( 30, 41)( 31, 44)( 32, 43)( 33, 46)( 34, 45)( 35, 48)( 36, 47)
( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 66)( 54, 65)( 55, 68)( 56, 67)
( 57, 70)( 58, 69)( 59, 72)( 60, 71)( 73, 86)( 74, 85)( 75, 88)( 76, 87)
( 77, 90)( 78, 89)( 79, 92)( 80, 91)( 81, 94)( 82, 93)( 83, 96)( 84, 95)
( 97,110)( 98,109)( 99,112)(100,111)(101,114)(102,113)(103,116)(104,115)
(105,118)(106,117)(107,120)(108,119)(121,134)(122,133)(123,136)(124,135)
(125,138)(126,137)(127,140)(128,139)(129,142)(130,141)(131,144)(132,143)
(145,158)(146,157)(147,160)(148,159)(149,162)(150,161)(151,164)(152,163)
(153,166)(154,165)(155,168)(156,167)(169,182)(170,181)(171,184)(172,183)
(173,186)(174,185)(175,188)(176,187)(177,190)(178,189)(179,192)(180,191);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s0*s1*s2*s3*s1*s0*s2*s3*s2*s1*s2*s3*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(192)!( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 43)
( 32, 44)( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 73, 85)( 74, 86)( 75, 87)
( 76, 88)( 77, 89)( 78, 90)( 79, 91)( 80, 92)( 81, 93)( 82, 94)( 83, 95)
( 84, 96)( 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)(121,181)(122,182)(123,183)(124,184)(125,185)(126,186)(127,187)
(128,188)(129,189)(130,190)(131,191)(132,192)(133,169)(134,170)(135,171)
(136,172)(137,173)(138,174)(139,175)(140,176)(141,177)(142,178)(143,179)
(144,180);
s1 := Sym(192)!( 1,121)( 2,122)( 3,124)( 4,123)( 5,129)( 6,130)( 7,132)
( 8,131)( 9,125)( 10,126)( 11,128)( 12,127)( 13,133)( 14,134)( 15,136)
( 16,135)( 17,141)( 18,142)( 19,144)( 20,143)( 21,137)( 22,138)( 23,140)
( 24,139)( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,105)( 30,106)( 31,108)
( 32,107)( 33,101)( 34,102)( 35,104)( 36,103)( 37,109)( 38,110)( 39,112)
( 40,111)( 41,117)( 42,118)( 43,120)( 44,119)( 45,113)( 46,114)( 47,116)
( 48,115)( 49,169)( 50,170)( 51,172)( 52,171)( 53,177)( 54,178)( 55,180)
( 56,179)( 57,173)( 58,174)( 59,176)( 60,175)( 61,181)( 62,182)( 63,184)
( 64,183)( 65,189)( 66,190)( 67,192)( 68,191)( 69,185)( 70,186)( 71,188)
( 72,187)( 73,145)( 74,146)( 75,148)( 76,147)( 77,153)( 78,154)( 79,156)
( 80,155)( 81,149)( 82,150)( 83,152)( 84,151)( 85,157)( 86,158)( 87,160)
( 88,159)( 89,165)( 90,166)( 91,168)( 92,167)( 93,161)( 94,162)( 95,164)
( 96,163);
s2 := Sym(192)!( 1, 9)( 2, 11)( 3, 10)( 4, 12)( 6, 7)( 13, 21)( 14, 23)
( 15, 22)( 16, 24)( 18, 19)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 41)
( 30, 43)( 31, 42)( 32, 44)( 33, 37)( 34, 39)( 35, 38)( 36, 40)( 49, 69)
( 50, 71)( 51, 70)( 52, 72)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 61)
( 58, 63)( 59, 62)( 60, 64)( 73, 81)( 74, 83)( 75, 82)( 76, 84)( 78, 79)
( 85, 93)( 86, 95)( 87, 94)( 88, 96)( 90, 91)( 97,129)( 98,131)( 99,130)
(100,132)(101,125)(102,127)(103,126)(104,128)(105,121)(106,123)(107,122)
(108,124)(109,141)(110,143)(111,142)(112,144)(113,137)(114,139)(115,138)
(116,140)(117,133)(118,135)(119,134)(120,136)(145,189)(146,191)(147,190)
(148,192)(149,185)(150,187)(151,186)(152,188)(153,181)(154,183)(155,182)
(156,184)(157,177)(158,179)(159,178)(160,180)(161,173)(162,175)(163,174)
(164,176)(165,169)(166,171)(167,170)(168,172);
s3 := Sym(192)!( 1, 14)( 2, 13)( 3, 16)( 4, 15)( 5, 18)( 6, 17)( 7, 20)
( 8, 19)( 9, 22)( 10, 21)( 11, 24)( 12, 23)( 25, 38)( 26, 37)( 27, 40)
( 28, 39)( 29, 42)( 30, 41)( 31, 44)( 32, 43)( 33, 46)( 34, 45)( 35, 48)
( 36, 47)( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 66)( 54, 65)( 55, 68)
( 56, 67)( 57, 70)( 58, 69)( 59, 72)( 60, 71)( 73, 86)( 74, 85)( 75, 88)
( 76, 87)( 77, 90)( 78, 89)( 79, 92)( 80, 91)( 81, 94)( 82, 93)( 83, 96)
( 84, 95)( 97,110)( 98,109)( 99,112)(100,111)(101,114)(102,113)(103,116)
(104,115)(105,118)(106,117)(107,120)(108,119)(121,134)(122,133)(123,136)
(124,135)(125,138)(126,137)(127,140)(128,139)(129,142)(130,141)(131,144)
(132,143)(145,158)(146,157)(147,160)(148,159)(149,162)(150,161)(151,164)
(152,163)(153,166)(154,165)(155,168)(156,167)(169,182)(170,181)(171,184)
(172,183)(173,186)(174,185)(175,188)(176,187)(177,190)(178,189)(179,192)
(180,191);
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, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s0*s1*s2*s3*s1*s0*s2*s3*s2*s1*s2*s3*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope