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