Polytope of Type {2,2,4,3,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,3,4}*768a
if this polytope has a name.
Group : SmallGroup(768,1090234)
Rank : 6
Schlafli Type : {2,2,4,3,4}
Number of vertices, edges, etc : 2, 2, 4, 12, 12, 8
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,2,4,3,4}*384
4-fold quotients : {2,2,4,3,2}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 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)(195,196);;
s3 := ( 5,117)( 6,120)( 7,119)( 8,118)( 9,125)( 10,128)( 11,127)( 12,126)
( 13,121)( 14,124)( 15,123)( 16,122)( 17,129)( 18,132)( 19,131)( 20,130)
( 21,101)( 22,104)( 23,103)( 24,102)( 25,109)( 26,112)( 27,111)( 28,110)
( 29,105)( 30,108)( 31,107)( 32,106)( 33,113)( 34,116)( 35,115)( 36,114)
( 37,133)( 38,136)( 39,135)( 40,134)( 41,141)( 42,144)( 43,143)( 44,142)
( 45,137)( 46,140)( 47,139)( 48,138)( 49,145)( 50,148)( 51,147)( 52,146)
( 53,165)( 54,168)( 55,167)( 56,166)( 57,173)( 58,176)( 59,175)( 60,174)
( 61,169)( 62,172)( 63,171)( 64,170)( 65,177)( 66,180)( 67,179)( 68,178)
( 69,149)( 70,152)( 71,151)( 72,150)( 73,157)( 74,160)( 75,159)( 76,158)
( 77,153)( 78,156)( 79,155)( 80,154)( 81,161)( 82,164)( 83,163)( 84,162)
( 85,181)( 86,184)( 87,183)( 88,182)( 89,189)( 90,192)( 91,191)( 92,190)
( 93,185)( 94,188)( 95,187)( 96,186)( 97,193)( 98,196)( 99,195)(100,194);;
s4 := ( 5,101)( 6,102)( 7,104)( 8,103)( 9,113)( 10,114)( 11,116)( 12,115)
( 13,109)( 14,110)( 15,112)( 16,111)( 17,105)( 18,106)( 19,108)( 20,107)
( 21,133)( 22,134)( 23,136)( 24,135)( 25,145)( 26,146)( 27,148)( 28,147)
( 29,141)( 30,142)( 31,144)( 32,143)( 33,137)( 34,138)( 35,140)( 36,139)
( 37,117)( 38,118)( 39,120)( 40,119)( 41,129)( 42,130)( 43,132)( 44,131)
( 45,125)( 46,126)( 47,128)( 48,127)( 49,121)( 50,122)( 51,124)( 52,123)
( 53,149)( 54,150)( 55,152)( 56,151)( 57,161)( 58,162)( 59,164)( 60,163)
( 61,157)( 62,158)( 63,160)( 64,159)( 65,153)( 66,154)( 67,156)( 68,155)
( 69,181)( 70,182)( 71,184)( 72,183)( 73,193)( 74,194)( 75,196)( 76,195)
( 77,189)( 78,190)( 79,192)( 80,191)( 81,185)( 82,186)( 83,188)( 84,187)
( 85,165)( 86,166)( 87,168)( 88,167)( 89,177)( 90,178)( 91,180)( 92,179)
( 93,173)( 94,174)( 95,176)( 96,175)( 97,169)( 98,170)( 99,172)(100,171);;
s5 := ( 5, 65)( 6, 66)( 7, 67)( 8, 68)( 9, 61)( 10, 62)( 11, 63)( 12, 64)
( 13, 57)( 14, 58)( 15, 59)( 16, 60)( 17, 53)( 18, 54)( 19, 55)( 20, 56)
( 21, 81)( 22, 82)( 23, 83)( 24, 84)( 25, 77)( 26, 78)( 27, 79)( 28, 80)
( 29, 73)( 30, 74)( 31, 75)( 32, 76)( 33, 69)( 34, 70)( 35, 71)( 36, 72)
( 37, 97)( 38, 98)( 39, 99)( 40,100)( 41, 93)( 42, 94)( 43, 95)( 44, 96)
( 45, 89)( 46, 90)( 47, 91)( 48, 92)( 49, 85)( 50, 86)( 51, 87)( 52, 88)
(101,161)(102,162)(103,163)(104,164)(105,157)(106,158)(107,159)(108,160)
(109,153)(110,154)(111,155)(112,156)(113,149)(114,150)(115,151)(116,152)
(117,177)(118,178)(119,179)(120,180)(121,173)(122,174)(123,175)(124,176)
(125,169)(126,170)(127,171)(128,172)(129,165)(130,166)(131,167)(132,168)
(133,193)(134,194)(135,195)(136,196)(137,189)(138,190)(139,191)(140,192)
(141,185)(142,186)(143,187)(144,188)(145,181)(146,182)(147,183)(148,184);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5*s4*s5, s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(196)!(1,2);
s1 := Sym(196)!(3,4);
s2 := Sym(196)!( 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)
(195,196);
s3 := Sym(196)!( 5,117)( 6,120)( 7,119)( 8,118)( 9,125)( 10,128)( 11,127)
( 12,126)( 13,121)( 14,124)( 15,123)( 16,122)( 17,129)( 18,132)( 19,131)
( 20,130)( 21,101)( 22,104)( 23,103)( 24,102)( 25,109)( 26,112)( 27,111)
( 28,110)( 29,105)( 30,108)( 31,107)( 32,106)( 33,113)( 34,116)( 35,115)
( 36,114)( 37,133)( 38,136)( 39,135)( 40,134)( 41,141)( 42,144)( 43,143)
( 44,142)( 45,137)( 46,140)( 47,139)( 48,138)( 49,145)( 50,148)( 51,147)
( 52,146)( 53,165)( 54,168)( 55,167)( 56,166)( 57,173)( 58,176)( 59,175)
( 60,174)( 61,169)( 62,172)( 63,171)( 64,170)( 65,177)( 66,180)( 67,179)
( 68,178)( 69,149)( 70,152)( 71,151)( 72,150)( 73,157)( 74,160)( 75,159)
( 76,158)( 77,153)( 78,156)( 79,155)( 80,154)( 81,161)( 82,164)( 83,163)
( 84,162)( 85,181)( 86,184)( 87,183)( 88,182)( 89,189)( 90,192)( 91,191)
( 92,190)( 93,185)( 94,188)( 95,187)( 96,186)( 97,193)( 98,196)( 99,195)
(100,194);
s4 := Sym(196)!( 5,101)( 6,102)( 7,104)( 8,103)( 9,113)( 10,114)( 11,116)
( 12,115)( 13,109)( 14,110)( 15,112)( 16,111)( 17,105)( 18,106)( 19,108)
( 20,107)( 21,133)( 22,134)( 23,136)( 24,135)( 25,145)( 26,146)( 27,148)
( 28,147)( 29,141)( 30,142)( 31,144)( 32,143)( 33,137)( 34,138)( 35,140)
( 36,139)( 37,117)( 38,118)( 39,120)( 40,119)( 41,129)( 42,130)( 43,132)
( 44,131)( 45,125)( 46,126)( 47,128)( 48,127)( 49,121)( 50,122)( 51,124)
( 52,123)( 53,149)( 54,150)( 55,152)( 56,151)( 57,161)( 58,162)( 59,164)
( 60,163)( 61,157)( 62,158)( 63,160)( 64,159)( 65,153)( 66,154)( 67,156)
( 68,155)( 69,181)( 70,182)( 71,184)( 72,183)( 73,193)( 74,194)( 75,196)
( 76,195)( 77,189)( 78,190)( 79,192)( 80,191)( 81,185)( 82,186)( 83,188)
( 84,187)( 85,165)( 86,166)( 87,168)( 88,167)( 89,177)( 90,178)( 91,180)
( 92,179)( 93,173)( 94,174)( 95,176)( 96,175)( 97,169)( 98,170)( 99,172)
(100,171);
s5 := Sym(196)!( 5, 65)( 6, 66)( 7, 67)( 8, 68)( 9, 61)( 10, 62)( 11, 63)
( 12, 64)( 13, 57)( 14, 58)( 15, 59)( 16, 60)( 17, 53)( 18, 54)( 19, 55)
( 20, 56)( 21, 81)( 22, 82)( 23, 83)( 24, 84)( 25, 77)( 26, 78)( 27, 79)
( 28, 80)( 29, 73)( 30, 74)( 31, 75)( 32, 76)( 33, 69)( 34, 70)( 35, 71)
( 36, 72)( 37, 97)( 38, 98)( 39, 99)( 40,100)( 41, 93)( 42, 94)( 43, 95)
( 44, 96)( 45, 89)( 46, 90)( 47, 91)( 48, 92)( 49, 85)( 50, 86)( 51, 87)
( 52, 88)(101,161)(102,162)(103,163)(104,164)(105,157)(106,158)(107,159)
(108,160)(109,153)(110,154)(111,155)(112,156)(113,149)(114,150)(115,151)
(116,152)(117,177)(118,178)(119,179)(120,180)(121,173)(122,174)(123,175)
(124,176)(125,169)(126,170)(127,171)(128,172)(129,165)(130,166)(131,167)
(132,168)(133,193)(134,194)(135,195)(136,196)(137,189)(138,190)(139,191)
(140,192)(141,185)(142,186)(143,187)(144,188)(145,181)(146,182)(147,183)
(148,184);
poly := sub<Sym(196)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5*s4*s5, s4*s2*s3*s4*s2*s3*s4*s2*s3 >;
to this polytope