Polytope of Type {4,39,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,39,4}*1248
if this polytope has a name.
Group : SmallGroup(1248,1443)
Rank : 4
Schlafli Type : {4,39,4}
Number of vertices, edges, etc : 4, 78, 78, 4
Order of s0s1s2s3 : 39
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
13-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17,193)( 18,194)
( 19,196)( 20,195)( 21,197)( 22,198)( 23,200)( 24,199)( 25,205)( 26,206)
( 27,208)( 28,207)( 29,201)( 30,202)( 31,204)( 32,203)( 33,177)( 34,178)
( 35,180)( 36,179)( 37,181)( 38,182)( 39,184)( 40,183)( 41,189)( 42,190)
( 43,192)( 44,191)( 45,185)( 46,186)( 47,188)( 48,187)( 49,161)( 50,162)
( 51,164)( 52,163)( 53,165)( 54,166)( 55,168)( 56,167)( 57,173)( 58,174)
( 59,176)( 60,175)( 61,169)( 62,170)( 63,172)( 64,171)( 65,145)( 66,146)
( 67,148)( 68,147)( 69,149)( 70,150)( 71,152)( 72,151)( 73,157)( 74,158)
( 75,160)( 76,159)( 77,153)( 78,154)( 79,156)( 80,155)( 81,129)( 82,130)
( 83,132)( 84,131)( 85,133)( 86,134)( 87,136)( 88,135)( 89,141)( 90,142)
( 91,144)( 92,143)( 93,137)( 94,138)( 95,140)( 96,139)( 97,113)( 98,114)
( 99,116)(100,115)(101,117)(102,118)(103,120)(104,119)(105,125)(106,126)
(107,128)(108,127)(109,121)(110,122)(111,124)(112,123);;
s2 := ( 1, 17)( 2, 20)( 3, 19)( 4, 18)( 5, 29)( 6, 32)( 7, 31)( 8, 30)
( 9, 25)( 10, 28)( 11, 27)( 12, 26)( 13, 21)( 14, 24)( 15, 23)( 16, 22)
( 33,193)( 34,196)( 35,195)( 36,194)( 37,205)( 38,208)( 39,207)( 40,206)
( 41,201)( 42,204)( 43,203)( 44,202)( 45,197)( 46,200)( 47,199)( 48,198)
( 49,177)( 50,180)( 51,179)( 52,178)( 53,189)( 54,192)( 55,191)( 56,190)
( 57,185)( 58,188)( 59,187)( 60,186)( 61,181)( 62,184)( 63,183)( 64,182)
( 65,161)( 66,164)( 67,163)( 68,162)( 69,173)( 70,176)( 71,175)( 72,174)
( 73,169)( 74,172)( 75,171)( 76,170)( 77,165)( 78,168)( 79,167)( 80,166)
( 81,145)( 82,148)( 83,147)( 84,146)( 85,157)( 86,160)( 87,159)( 88,158)
( 89,153)( 90,156)( 91,155)( 92,154)( 93,149)( 94,152)( 95,151)( 96,150)
( 97,129)( 98,132)( 99,131)(100,130)(101,141)(102,144)(103,143)(104,142)
(105,137)(106,140)(107,139)(108,138)(109,133)(110,136)(111,135)(112,134)
(114,116)(117,125)(118,128)(119,127)(120,126)(122,124);;
s3 := ( 1, 2)( 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)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(208)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208);
s1 := Sym(208)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17,193)
( 18,194)( 19,196)( 20,195)( 21,197)( 22,198)( 23,200)( 24,199)( 25,205)
( 26,206)( 27,208)( 28,207)( 29,201)( 30,202)( 31,204)( 32,203)( 33,177)
( 34,178)( 35,180)( 36,179)( 37,181)( 38,182)( 39,184)( 40,183)( 41,189)
( 42,190)( 43,192)( 44,191)( 45,185)( 46,186)( 47,188)( 48,187)( 49,161)
( 50,162)( 51,164)( 52,163)( 53,165)( 54,166)( 55,168)( 56,167)( 57,173)
( 58,174)( 59,176)( 60,175)( 61,169)( 62,170)( 63,172)( 64,171)( 65,145)
( 66,146)( 67,148)( 68,147)( 69,149)( 70,150)( 71,152)( 72,151)( 73,157)
( 74,158)( 75,160)( 76,159)( 77,153)( 78,154)( 79,156)( 80,155)( 81,129)
( 82,130)( 83,132)( 84,131)( 85,133)( 86,134)( 87,136)( 88,135)( 89,141)
( 90,142)( 91,144)( 92,143)( 93,137)( 94,138)( 95,140)( 96,139)( 97,113)
( 98,114)( 99,116)(100,115)(101,117)(102,118)(103,120)(104,119)(105,125)
(106,126)(107,128)(108,127)(109,121)(110,122)(111,124)(112,123);
s2 := Sym(208)!( 1, 17)( 2, 20)( 3, 19)( 4, 18)( 5, 29)( 6, 32)( 7, 31)
( 8, 30)( 9, 25)( 10, 28)( 11, 27)( 12, 26)( 13, 21)( 14, 24)( 15, 23)
( 16, 22)( 33,193)( 34,196)( 35,195)( 36,194)( 37,205)( 38,208)( 39,207)
( 40,206)( 41,201)( 42,204)( 43,203)( 44,202)( 45,197)( 46,200)( 47,199)
( 48,198)( 49,177)( 50,180)( 51,179)( 52,178)( 53,189)( 54,192)( 55,191)
( 56,190)( 57,185)( 58,188)( 59,187)( 60,186)( 61,181)( 62,184)( 63,183)
( 64,182)( 65,161)( 66,164)( 67,163)( 68,162)( 69,173)( 70,176)( 71,175)
( 72,174)( 73,169)( 74,172)( 75,171)( 76,170)( 77,165)( 78,168)( 79,167)
( 80,166)( 81,145)( 82,148)( 83,147)( 84,146)( 85,157)( 86,160)( 87,159)
( 88,158)( 89,153)( 90,156)( 91,155)( 92,154)( 93,149)( 94,152)( 95,151)
( 96,150)( 97,129)( 98,132)( 99,131)(100,130)(101,141)(102,144)(103,143)
(104,142)(105,137)(106,140)(107,139)(108,138)(109,133)(110,136)(111,135)
(112,134)(114,116)(117,125)(118,128)(119,127)(120,126)(122,124);
s3 := Sym(208)!( 1, 2)( 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)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208);
poly := sub<Sym(208)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope