Polytope of Type {8,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12,4}*768c
if this polytope has a name.
Group : SmallGroup(768,1087755)
Rank : 4
Schlafli Type : {8,12,4}
Number of vertices, edges, etc : 8, 48, 24, 4
Order of s0s1s2s3 : 24
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 : {4,12,4}*384b, {8,6,4}*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 := ( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 67)( 56, 68)
( 57, 69)( 58, 70)( 59, 71)( 60, 72)( 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)
(121,169)(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);;
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)
( 49,181)( 50,182)( 51,184)( 52,183)( 53,189)( 54,190)( 55,192)( 56,191)
( 57,185)( 58,186)( 59,188)( 60,187)( 61,169)( 62,170)( 63,172)( 64,171)
( 65,177)( 66,178)( 67,180)( 68,179)( 69,173)( 70,174)( 71,176)( 72,175)
( 73,157)( 74,158)( 75,160)( 76,159)( 77,165)( 78,166)( 79,168)( 80,167)
( 81,161)( 82,162)( 83,164)( 84,163)( 85,145)( 86,146)( 87,148)( 88,147)
( 89,153)( 90,154)( 91,156)( 92,155)( 93,149)( 94,150)( 95,152)( 96,151);;
s2 := ( 1, 9)( 2, 11)( 3, 10)( 4, 12)( 6, 7)( 13, 21)( 14, 23)( 15, 22)
( 16, 24)( 18, 19)( 25, 33)( 26, 35)( 27, 34)( 28, 36)( 30, 31)( 37, 45)
( 38, 47)( 39, 46)( 40, 48)( 42, 43)( 49, 57)( 50, 59)( 51, 58)( 52, 60)
( 54, 55)( 61, 69)( 62, 71)( 63, 70)( 64, 72)( 66, 67)( 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)
(145,177)(146,179)(147,178)(148,180)(149,173)(150,175)(151,174)(152,176)
(153,169)(154,171)(155,170)(156,172)(157,189)(158,191)(159,190)(160,192)
(161,185)(162,187)(163,186)(164,188)(165,181)(166,183)(167,182)(168,184);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192);;
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*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(192)!( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 67)
( 56, 68)( 57, 69)( 58, 70)( 59, 71)( 60, 72)( 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)(121,169)(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);
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)( 49,181)( 50,182)( 51,184)( 52,183)( 53,189)( 54,190)( 55,192)
( 56,191)( 57,185)( 58,186)( 59,188)( 60,187)( 61,169)( 62,170)( 63,172)
( 64,171)( 65,177)( 66,178)( 67,180)( 68,179)( 69,173)( 70,174)( 71,176)
( 72,175)( 73,157)( 74,158)( 75,160)( 76,159)( 77,165)( 78,166)( 79,168)
( 80,167)( 81,161)( 82,162)( 83,164)( 84,163)( 85,145)( 86,146)( 87,148)
( 88,147)( 89,153)( 90,154)( 91,156)( 92,155)( 93,149)( 94,150)( 95,152)
( 96,151);
s2 := Sym(192)!( 1, 9)( 2, 11)( 3, 10)( 4, 12)( 6, 7)( 13, 21)( 14, 23)
( 15, 22)( 16, 24)( 18, 19)( 25, 33)( 26, 35)( 27, 34)( 28, 36)( 30, 31)
( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 42, 43)( 49, 57)( 50, 59)( 51, 58)
( 52, 60)( 54, 55)( 61, 69)( 62, 71)( 63, 70)( 64, 72)( 66, 67)( 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)(145,177)(146,179)(147,178)(148,180)(149,173)(150,175)(151,174)
(152,176)(153,169)(154,171)(155,170)(156,172)(157,189)(158,191)(159,190)
(160,192)(161,185)(162,187)(163,186)(164,188)(165,181)(166,183)(167,182)
(168,184);
s3 := Sym(192)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192);
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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 >;
References : None.
to this polytope