Polytope of Type {2,2,4,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,6,4}*768d
if this polytope has a name.
Group : SmallGroup(768,1090234)
Rank : 6
Schlafli Type : {2,2,4,6,4}
Number of vertices, edges, etc : 2, 2, 4, 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
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 := ( 5,149)( 6,150)( 7,152)( 8,151)( 9,161)( 10,162)( 11,164)( 12,163)
( 13,157)( 14,158)( 15,160)( 16,159)( 17,153)( 18,154)( 19,156)( 20,155)
( 21,181)( 22,182)( 23,184)( 24,183)( 25,193)( 26,194)( 27,196)( 28,195)
( 29,189)( 30,190)( 31,192)( 32,191)( 33,185)( 34,186)( 35,188)( 36,187)
( 37,165)( 38,166)( 39,168)( 40,167)( 41,177)( 42,178)( 43,180)( 44,179)
( 45,173)( 46,174)( 47,176)( 48,175)( 49,169)( 50,170)( 51,172)( 52,171)
( 53,101)( 54,102)( 55,104)( 56,103)( 57,113)( 58,114)( 59,116)( 60,115)
( 61,109)( 62,110)( 63,112)( 64,111)( 65,105)( 66,106)( 67,108)( 68,107)
( 69,133)( 70,134)( 71,136)( 72,135)( 73,145)( 74,146)( 75,148)( 76,147)
( 77,141)( 78,142)( 79,144)( 80,143)( 81,137)( 82,138)( 83,140)( 84,139)
( 85,117)( 86,118)( 87,120)( 88,119)( 89,129)( 90,130)( 91,132)( 92,131)
( 93,125)( 94,126)( 95,128)( 96,127)( 97,121)( 98,122)( 99,124)(100,123);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5,
s2*s3*s4*s3*s2*s3*s4*s2*s3, s5*s4*s3*s5*s4*s5*s4*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)!( 5,149)( 6,150)( 7,152)( 8,151)( 9,161)( 10,162)( 11,164)
( 12,163)( 13,157)( 14,158)( 15,160)( 16,159)( 17,153)( 18,154)( 19,156)
( 20,155)( 21,181)( 22,182)( 23,184)( 24,183)( 25,193)( 26,194)( 27,196)
( 28,195)( 29,189)( 30,190)( 31,192)( 32,191)( 33,185)( 34,186)( 35,188)
( 36,187)( 37,165)( 38,166)( 39,168)( 40,167)( 41,177)( 42,178)( 43,180)
( 44,179)( 45,173)( 46,174)( 47,176)( 48,175)( 49,169)( 50,170)( 51,172)
( 52,171)( 53,101)( 54,102)( 55,104)( 56,103)( 57,113)( 58,114)( 59,116)
( 60,115)( 61,109)( 62,110)( 63,112)( 64,111)( 65,105)( 66,106)( 67,108)
( 68,107)( 69,133)( 70,134)( 71,136)( 72,135)( 73,145)( 74,146)( 75,148)
( 76,147)( 77,141)( 78,142)( 79,144)( 80,143)( 81,137)( 82,138)( 83,140)
( 84,139)( 85,117)( 86,118)( 87,120)( 88,119)( 89,129)( 90,130)( 91,132)
( 92,131)( 93,125)( 94,126)( 95,128)( 96,127)( 97,121)( 98,122)( 99,124)
(100,123);
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, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s2*s3,
s5*s4*s3*s5*s4*s5*s4*s3*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope