Polytope of Type {4,3,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,4,2}*384b
if this polytope has a name.
Group : SmallGroup(384,20163)
Rank : 5
Schlafli Type : {4,3,4,2}
Number of vertices, edges, etc : 8, 12, 12, 4, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,3,4,2,2} of size 768
{4,3,4,2,3} of size 1152
{4,3,4,2,5} of size 1920
Vertex Figure Of :
{2,4,3,4,2} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,3,4,2}*192
4-fold quotients : {2,3,4,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,3,4,2}*768, {4,3,4,2}*768, {4,6,4,2}*768d, {4,6,4,2}*768e
3-fold covers : {4,9,4,2}*1152b, {12,3,4,2}*1152
5-fold covers : {4,15,4,2}*1920b
Permutation Representation (GAP) :
s0 := ( 1, 50)( 2, 49)( 3, 52)( 4, 51)( 5, 54)( 6, 53)( 7, 56)( 8, 55)
( 9, 58)( 10, 57)( 11, 60)( 12, 59)( 13, 62)( 14, 61)( 15, 64)( 16, 63)
( 17, 66)( 18, 65)( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 72)( 24, 71)
( 25, 74)( 26, 73)( 27, 76)( 28, 75)( 29, 78)( 30, 77)( 31, 80)( 32, 79)
( 33, 82)( 34, 81)( 35, 84)( 36, 83)( 37, 86)( 38, 85)( 39, 88)( 40, 87)
( 41, 90)( 42, 89)( 43, 92)( 44, 91)( 45, 94)( 46, 93)( 47, 96)( 48, 95)
( 97,146)( 98,145)( 99,148)(100,147)(101,150)(102,149)(103,152)(104,151)
(105,154)(106,153)(107,156)(108,155)(109,158)(110,157)(111,160)(112,159)
(113,162)(114,161)(115,164)(116,163)(117,166)(118,165)(119,168)(120,167)
(121,170)(122,169)(123,172)(124,171)(125,174)(126,173)(127,176)(128,175)
(129,178)(130,177)(131,180)(132,179)(133,182)(134,181)(135,184)(136,183)
(137,186)(138,185)(139,188)(140,187)(141,190)(142,189)(143,192)(144,191);;
s1 := ( 1,113)( 2,116)( 3,115)( 4,114)( 5,121)( 6,124)( 7,123)( 8,122)
( 9,117)( 10,120)( 11,119)( 12,118)( 13,125)( 14,128)( 15,127)( 16,126)
( 17, 97)( 18,100)( 19, 99)( 20, 98)( 21,105)( 22,108)( 23,107)( 24,106)
( 25,101)( 26,104)( 27,103)( 28,102)( 29,109)( 30,112)( 31,111)( 32,110)
( 33,129)( 34,132)( 35,131)( 36,130)( 37,137)( 38,140)( 39,139)( 40,138)
( 41,133)( 42,136)( 43,135)( 44,134)( 45,141)( 46,144)( 47,143)( 48,142)
( 49,161)( 50,164)( 51,163)( 52,162)( 53,169)( 54,172)( 55,171)( 56,170)
( 57,165)( 58,168)( 59,167)( 60,166)( 61,173)( 62,176)( 63,175)( 64,174)
( 65,145)( 66,148)( 67,147)( 68,146)( 69,153)( 70,156)( 71,155)( 72,154)
( 73,149)( 74,152)( 75,151)( 76,150)( 77,157)( 78,160)( 79,159)( 80,158)
( 81,177)( 82,180)( 83,179)( 84,178)( 85,185)( 86,188)( 87,187)( 88,186)
( 89,181)( 90,184)( 91,183)( 92,182)( 93,189)( 94,192)( 95,191)( 96,190);;
s2 := ( 1, 97)( 2, 98)( 3,100)( 4, 99)( 5,109)( 6,110)( 7,112)( 8,111)
( 9,105)( 10,106)( 11,108)( 12,107)( 13,101)( 14,102)( 15,104)( 16,103)
( 17,129)( 18,130)( 19,132)( 20,131)( 21,141)( 22,142)( 23,144)( 24,143)
( 25,137)( 26,138)( 27,140)( 28,139)( 29,133)( 30,134)( 31,136)( 32,135)
( 33,113)( 34,114)( 35,116)( 36,115)( 37,125)( 38,126)( 39,128)( 40,127)
( 41,121)( 42,122)( 43,124)( 44,123)( 45,117)( 46,118)( 47,120)( 48,119)
( 49,145)( 50,146)( 51,148)( 52,147)( 53,157)( 54,158)( 55,160)( 56,159)
( 57,153)( 58,154)( 59,156)( 60,155)( 61,149)( 62,150)( 63,152)( 64,151)
( 65,177)( 66,178)( 67,180)( 68,179)( 69,189)( 70,190)( 71,192)( 72,191)
( 73,185)( 74,186)( 75,188)( 76,187)( 77,181)( 78,182)( 79,184)( 80,183)
( 81,161)( 82,162)( 83,164)( 84,163)( 85,173)( 86,174)( 87,176)( 88,175)
( 89,169)( 90,170)( 91,172)( 92,171)( 93,165)( 94,166)( 95,168)( 96,167);;
s3 := ( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 9)( 6, 10)( 7, 11)( 8, 12)
( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)( 24, 28)
( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 41)( 38, 42)( 39, 43)( 40, 44)
( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)( 56, 60)
( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)
( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 89)( 86, 90)( 87, 91)( 88, 92)
( 97,109)( 98,110)( 99,111)(100,112)(101,105)(102,106)(103,107)(104,108)
(113,125)(114,126)(115,127)(116,128)(117,121)(118,122)(119,123)(120,124)
(129,141)(130,142)(131,143)(132,144)(133,137)(134,138)(135,139)(136,140)
(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)(152,156)
(161,173)(162,174)(163,175)(164,176)(165,169)(166,170)(167,171)(168,172)
(177,189)(178,190)(179,191)(180,192)(181,185)(182,186)(183,187)(184,188);;
s4 := (193,194);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!( 1, 50)( 2, 49)( 3, 52)( 4, 51)( 5, 54)( 6, 53)( 7, 56)
( 8, 55)( 9, 58)( 10, 57)( 11, 60)( 12, 59)( 13, 62)( 14, 61)( 15, 64)
( 16, 63)( 17, 66)( 18, 65)( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 72)
( 24, 71)( 25, 74)( 26, 73)( 27, 76)( 28, 75)( 29, 78)( 30, 77)( 31, 80)
( 32, 79)( 33, 82)( 34, 81)( 35, 84)( 36, 83)( 37, 86)( 38, 85)( 39, 88)
( 40, 87)( 41, 90)( 42, 89)( 43, 92)( 44, 91)( 45, 94)( 46, 93)( 47, 96)
( 48, 95)( 97,146)( 98,145)( 99,148)(100,147)(101,150)(102,149)(103,152)
(104,151)(105,154)(106,153)(107,156)(108,155)(109,158)(110,157)(111,160)
(112,159)(113,162)(114,161)(115,164)(116,163)(117,166)(118,165)(119,168)
(120,167)(121,170)(122,169)(123,172)(124,171)(125,174)(126,173)(127,176)
(128,175)(129,178)(130,177)(131,180)(132,179)(133,182)(134,181)(135,184)
(136,183)(137,186)(138,185)(139,188)(140,187)(141,190)(142,189)(143,192)
(144,191);
s1 := Sym(194)!( 1,113)( 2,116)( 3,115)( 4,114)( 5,121)( 6,124)( 7,123)
( 8,122)( 9,117)( 10,120)( 11,119)( 12,118)( 13,125)( 14,128)( 15,127)
( 16,126)( 17, 97)( 18,100)( 19, 99)( 20, 98)( 21,105)( 22,108)( 23,107)
( 24,106)( 25,101)( 26,104)( 27,103)( 28,102)( 29,109)( 30,112)( 31,111)
( 32,110)( 33,129)( 34,132)( 35,131)( 36,130)( 37,137)( 38,140)( 39,139)
( 40,138)( 41,133)( 42,136)( 43,135)( 44,134)( 45,141)( 46,144)( 47,143)
( 48,142)( 49,161)( 50,164)( 51,163)( 52,162)( 53,169)( 54,172)( 55,171)
( 56,170)( 57,165)( 58,168)( 59,167)( 60,166)( 61,173)( 62,176)( 63,175)
( 64,174)( 65,145)( 66,148)( 67,147)( 68,146)( 69,153)( 70,156)( 71,155)
( 72,154)( 73,149)( 74,152)( 75,151)( 76,150)( 77,157)( 78,160)( 79,159)
( 80,158)( 81,177)( 82,180)( 83,179)( 84,178)( 85,185)( 86,188)( 87,187)
( 88,186)( 89,181)( 90,184)( 91,183)( 92,182)( 93,189)( 94,192)( 95,191)
( 96,190);
s2 := Sym(194)!( 1, 97)( 2, 98)( 3,100)( 4, 99)( 5,109)( 6,110)( 7,112)
( 8,111)( 9,105)( 10,106)( 11,108)( 12,107)( 13,101)( 14,102)( 15,104)
( 16,103)( 17,129)( 18,130)( 19,132)( 20,131)( 21,141)( 22,142)( 23,144)
( 24,143)( 25,137)( 26,138)( 27,140)( 28,139)( 29,133)( 30,134)( 31,136)
( 32,135)( 33,113)( 34,114)( 35,116)( 36,115)( 37,125)( 38,126)( 39,128)
( 40,127)( 41,121)( 42,122)( 43,124)( 44,123)( 45,117)( 46,118)( 47,120)
( 48,119)( 49,145)( 50,146)( 51,148)( 52,147)( 53,157)( 54,158)( 55,160)
( 56,159)( 57,153)( 58,154)( 59,156)( 60,155)( 61,149)( 62,150)( 63,152)
( 64,151)( 65,177)( 66,178)( 67,180)( 68,179)( 69,189)( 70,190)( 71,192)
( 72,191)( 73,185)( 74,186)( 75,188)( 76,187)( 77,181)( 78,182)( 79,184)
( 80,183)( 81,161)( 82,162)( 83,164)( 84,163)( 85,173)( 86,174)( 87,176)
( 88,175)( 89,169)( 90,170)( 91,172)( 92,171)( 93,165)( 94,166)( 95,168)
( 96,167);
s3 := Sym(194)!( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 9)( 6, 10)( 7, 11)
( 8, 12)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)
( 24, 28)( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 41)( 38, 42)( 39, 43)
( 40, 44)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)
( 56, 60)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)
( 72, 76)( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 89)( 86, 90)( 87, 91)
( 88, 92)( 97,109)( 98,110)( 99,111)(100,112)(101,105)(102,106)(103,107)
(104,108)(113,125)(114,126)(115,127)(116,128)(117,121)(118,122)(119,123)
(120,124)(129,141)(130,142)(131,143)(132,144)(133,137)(134,138)(135,139)
(136,140)(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)
(152,156)(161,173)(162,174)(163,175)(164,176)(165,169)(166,170)(167,171)
(168,172)(177,189)(178,190)(179,191)(180,192)(181,185)(182,186)(183,187)
(184,188);
s4 := Sym(194)!(193,194);
poly := sub<Sym(194)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s3*s2*s1*s3*s2*s1*s3*s2 >;
to this polytope