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