Polytope of Type {2,4,14,7}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,14,7}*1568
if this polytope has a name.
Group : SmallGroup(1568,877)
Rank : 5
Schlafli Type : {2,4,14,7}
Number of vertices, edges, etc : 2, 4, 28, 49, 7
Order of s0s1s2s3s4 : 28
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
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 : {2,2,14,7}*784
7-fold quotients : {2,4,2,7}*224
14-fold quotients : {2,2,2,7}*112
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,101)( 4,102)( 5,103)( 6,104)( 7,105)( 8,106)( 9,107)( 10,108)
( 11,109)( 12,110)( 13,111)( 14,112)( 15,113)( 16,114)( 17,115)( 18,116)
( 19,117)( 20,118)( 21,119)( 22,120)( 23,121)( 24,122)( 25,123)( 26,124)
( 27,125)( 28,126)( 29,127)( 30,128)( 31,129)( 32,130)( 33,131)( 34,132)
( 35,133)( 36,134)( 37,135)( 38,136)( 39,137)( 40,138)( 41,139)( 42,140)
( 43,141)( 44,142)( 45,143)( 46,144)( 47,145)( 48,146)( 49,147)( 50,148)
( 51,149)( 52,150)( 53,151)( 54,152)( 55,153)( 56,154)( 57,155)( 58,156)
( 59,157)( 60,158)( 61,159)( 62,160)( 63,161)( 64,162)( 65,163)( 66,164)
( 67,165)( 68,166)( 69,167)( 70,168)( 71,169)( 72,170)( 73,171)( 74,172)
( 75,173)( 76,174)( 77,175)( 78,176)( 79,177)( 80,178)( 81,179)( 82,180)
( 83,181)( 84,182)( 85,183)( 86,184)( 87,185)( 88,186)( 89,187)( 90,188)
( 91,189)( 92,190)( 93,191)( 94,192)( 95,193)( 96,194)( 97,195)( 98,196)
( 99,197)(100,198);;
s2 := ( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)
( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)
( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)
( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)( 75, 78)
( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)( 95,100)
( 96, 99)( 97, 98)(101,150)(102,156)(103,155)(104,154)(105,153)(106,152)
(107,151)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)(114,158)
(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,171)
(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,178)(130,184)
(131,183)(132,182)(133,181)(134,180)(135,179)(136,185)(137,191)(138,190)
(139,189)(140,188)(141,187)(142,186)(143,192)(144,198)(145,197)(146,196)
(147,195)(148,194)(149,193);;
s3 := ( 3, 4)( 5, 9)( 6, 8)( 10, 46)( 11, 45)( 12, 51)( 13, 50)( 14, 49)
( 15, 48)( 16, 47)( 17, 39)( 18, 38)( 19, 44)( 20, 43)( 21, 42)( 22, 41)
( 23, 40)( 24, 32)( 25, 31)( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)
( 52, 53)( 54, 58)( 55, 57)( 59, 95)( 60, 94)( 61,100)( 62, 99)( 63, 98)
( 64, 97)( 65, 96)( 66, 88)( 67, 87)( 68, 93)( 69, 92)( 70, 91)( 71, 90)
( 72, 89)( 73, 81)( 74, 80)( 75, 86)( 76, 85)( 77, 84)( 78, 83)( 79, 82)
(101,102)(103,107)(104,106)(108,144)(109,143)(110,149)(111,148)(112,147)
(113,146)(114,145)(115,137)(116,136)(117,142)(118,141)(119,140)(120,139)
(121,138)(122,130)(123,129)(124,135)(125,134)(126,133)(127,132)(128,131)
(150,151)(152,156)(153,155)(157,193)(158,192)(159,198)(160,197)(161,196)
(162,195)(163,194)(164,186)(165,185)(166,191)(167,190)(168,189)(169,188)
(170,187)(171,179)(172,178)(173,184)(174,183)(175,182)(176,181)(177,180);;
s4 := ( 3, 10)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)( 17, 45)
( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 38)( 25, 44)
( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 32, 37)( 33, 36)( 34, 35)
( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 66, 94)
( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 72, 95)( 73, 87)( 74, 93)
( 75, 92)( 76, 91)( 77, 90)( 78, 89)( 79, 88)( 81, 86)( 82, 85)( 83, 84)
(101,108)(102,114)(103,113)(104,112)(105,111)(106,110)(107,109)(115,143)
(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,136)(123,142)
(124,141)(125,140)(126,139)(127,138)(128,137)(130,135)(131,134)(132,133)
(150,157)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(164,192)
(165,198)(166,197)(167,196)(168,195)(169,194)(170,193)(171,185)(172,191)
(173,190)(174,189)(175,188)(176,187)(177,186)(179,184)(180,183)(181,182);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(198)!(1,2);
s1 := Sym(198)!( 3,101)( 4,102)( 5,103)( 6,104)( 7,105)( 8,106)( 9,107)
( 10,108)( 11,109)( 12,110)( 13,111)( 14,112)( 15,113)( 16,114)( 17,115)
( 18,116)( 19,117)( 20,118)( 21,119)( 22,120)( 23,121)( 24,122)( 25,123)
( 26,124)( 27,125)( 28,126)( 29,127)( 30,128)( 31,129)( 32,130)( 33,131)
( 34,132)( 35,133)( 36,134)( 37,135)( 38,136)( 39,137)( 40,138)( 41,139)
( 42,140)( 43,141)( 44,142)( 45,143)( 46,144)( 47,145)( 48,146)( 49,147)
( 50,148)( 51,149)( 52,150)( 53,151)( 54,152)( 55,153)( 56,154)( 57,155)
( 58,156)( 59,157)( 60,158)( 61,159)( 62,160)( 63,161)( 64,162)( 65,163)
( 66,164)( 67,165)( 68,166)( 69,167)( 70,168)( 71,169)( 72,170)( 73,171)
( 74,172)( 75,173)( 76,174)( 77,175)( 78,176)( 79,177)( 80,178)( 81,179)
( 82,180)( 83,181)( 84,182)( 85,183)( 86,184)( 87,185)( 88,186)( 89,187)
( 90,188)( 91,189)( 92,190)( 93,191)( 94,192)( 95,193)( 96,194)( 97,195)
( 98,196)( 99,197)(100,198);
s2 := Sym(198)!( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)
( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)
( 39, 44)( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)
( 55, 56)( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)
( 75, 78)( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)
( 95,100)( 96, 99)( 97, 98)(101,150)(102,156)(103,155)(104,154)(105,153)
(106,152)(107,151)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)
(114,158)(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)
(122,171)(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,178)
(130,184)(131,183)(132,182)(133,181)(134,180)(135,179)(136,185)(137,191)
(138,190)(139,189)(140,188)(141,187)(142,186)(143,192)(144,198)(145,197)
(146,196)(147,195)(148,194)(149,193);
s3 := Sym(198)!( 3, 4)( 5, 9)( 6, 8)( 10, 46)( 11, 45)( 12, 51)( 13, 50)
( 14, 49)( 15, 48)( 16, 47)( 17, 39)( 18, 38)( 19, 44)( 20, 43)( 21, 42)
( 22, 41)( 23, 40)( 24, 32)( 25, 31)( 26, 37)( 27, 36)( 28, 35)( 29, 34)
( 30, 33)( 52, 53)( 54, 58)( 55, 57)( 59, 95)( 60, 94)( 61,100)( 62, 99)
( 63, 98)( 64, 97)( 65, 96)( 66, 88)( 67, 87)( 68, 93)( 69, 92)( 70, 91)
( 71, 90)( 72, 89)( 73, 81)( 74, 80)( 75, 86)( 76, 85)( 77, 84)( 78, 83)
( 79, 82)(101,102)(103,107)(104,106)(108,144)(109,143)(110,149)(111,148)
(112,147)(113,146)(114,145)(115,137)(116,136)(117,142)(118,141)(119,140)
(120,139)(121,138)(122,130)(123,129)(124,135)(125,134)(126,133)(127,132)
(128,131)(150,151)(152,156)(153,155)(157,193)(158,192)(159,198)(160,197)
(161,196)(162,195)(163,194)(164,186)(165,185)(166,191)(167,190)(168,189)
(169,188)(170,187)(171,179)(172,178)(173,184)(174,183)(175,182)(176,181)
(177,180);
s4 := Sym(198)!( 3, 10)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)
( 17, 45)( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 38)
( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 32, 37)( 33, 36)
( 34, 35)( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)
( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 72, 95)( 73, 87)
( 74, 93)( 75, 92)( 76, 91)( 77, 90)( 78, 89)( 79, 88)( 81, 86)( 82, 85)
( 83, 84)(101,108)(102,114)(103,113)(104,112)(105,111)(106,110)(107,109)
(115,143)(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,136)
(123,142)(124,141)(125,140)(126,139)(127,138)(128,137)(130,135)(131,134)
(132,133)(150,157)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)
(164,192)(165,198)(166,197)(167,196)(168,195)(169,194)(170,193)(171,185)
(172,191)(173,190)(174,189)(175,188)(176,187)(177,186)(179,184)(180,183)
(181,182);
poly := sub<Sym(198)|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,
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope