Polytope of Type {14,14,4} with group SmallGroup(1568,858)

Overview

Group: SmallGroup(1568,858)
Rank: 4
Schläfli Type: {14,14,4}
Vertices, edges, …: 14, 98, 28, 4
Order of s₀s₁s₂s₃: 28
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{14,14|2},{14,4|2}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{14,14,2}*784a

7-fold

14-fold

28-fold

49-fold

{2,2,4}*32

98-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 36)( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 57, 92)( 58, 93)( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)( 67, 88)( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)(111,146)(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)(164,185)(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182);;
s1 := (  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 15, 43)( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)( 23, 42)( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)( 32, 33)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)( 81, 82)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,141)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,134)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)(130,131)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(177,182)(178,181)(179,180);;
s2 := (  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)( 94, 98)( 95, 97)( 99,149)(100,148)(101,154)(102,153)(103,152)(104,151)(105,150)(106,156)(107,155)(108,161)(109,160)(110,159)(111,158)(112,157)(113,163)(114,162)(115,168)(116,167)(117,166)(118,165)(119,164)(120,170)(121,169)(122,175)(123,174)(124,173)(125,172)(126,171)(127,177)(128,176)(129,182)(130,181)(131,180)(132,179)(133,178)(134,184)(135,183)(136,189)(137,188)(138,187)(139,186)(140,185)(141,191)(142,190)(143,196)(144,195)(145,194)(146,193)(147,192);;
s3 := (  1, 99)(  2,100)(  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);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(196)!(  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 36)( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 57, 92)( 58, 93)( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)( 67, 88)( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)(111,146)(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)(164,185)(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182);
s1 := Sym(196)!(  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 15, 43)( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)( 23, 42)( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)( 32, 33)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)( 81, 82)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,141)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,134)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)(130,131)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(177,182)(178,181)(179,180);
s2 := Sym(196)!(  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)( 94, 98)( 95, 97)( 99,149)(100,148)(101,154)(102,153)(103,152)(104,151)(105,150)(106,156)(107,155)(108,161)(109,160)(110,159)(111,158)(112,157)(113,163)(114,162)(115,168)(116,167)(117,166)(118,165)(119,164)(120,170)(121,169)(122,175)(123,174)(124,173)(125,172)(126,171)(127,177)(128,176)(129,182)(130,181)(131,180)(132,179)(133,178)(134,184)(135,183)(136,189)(137,188)(138,187)(139,186)(140,185)(141,191)(142,190)(143,196)(144,195)(145,194)(146,193)(147,192);
s3 := Sym(196)!(  1, 99)(  2,100)(  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);
poly := sub<Sym(196)|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*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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