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