Overview
- Group
- SmallGroup(1632,1097)
- Rank
- 4
- Schläfli Type
- {4,34,6}
- Vertices, edges, …
- 4, 68, 102, 6
- Order of s0s1s2s3
- 204
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{4,34|2},{34,6|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
12-fold
17-fold
34-fold
51-fold
68-fold
102-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := (103,154)(104,155)(105,156)(106,157)(107,158)(108,159)(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)(117,168)(118,169)(119,170)(120,171)(121,172)(122,173)(123,174)(124,175)(125,176)(126,177)(127,178)(128,179)(129,180)(130,181)(131,182)(132,183)(133,184)(134,185)(135,186)(136,187)(137,188)(138,189)(139,190)(140,191)(141,192)(142,193)(143,194)(144,195)(145,196)(146,197)(147,198)(148,199)(149,200)(150,201)(151,202)(152,203)(153,204);; s1 := ( 1,103)( 2,119)( 3,118)( 4,117)( 5,116)( 6,115)( 7,114)( 8,113)( 9,112)( 10,111)( 11,110)( 12,109)( 13,108)( 14,107)( 15,106)( 16,105)( 17,104)( 18,120)( 19,136)( 20,135)( 21,134)( 22,133)( 23,132)( 24,131)( 25,130)( 26,129)( 27,128)( 28,127)( 29,126)( 30,125)( 31,124)( 32,123)( 33,122)( 34,121)( 35,137)( 36,153)( 37,152)( 38,151)( 39,150)( 40,149)( 41,148)( 42,147)( 43,146)( 44,145)( 45,144)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,154)( 53,170)( 54,169)( 55,168)( 56,167)( 57,166)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)( 64,159)( 65,158)( 66,157)( 67,156)( 68,155)( 69,171)( 70,187)( 71,186)( 72,185)( 73,184)( 74,183)( 75,182)( 76,181)( 77,180)( 78,179)( 79,178)( 80,177)( 81,176)( 82,175)( 83,174)( 84,173)( 85,172)( 86,188)( 87,204)( 88,203)( 89,202)( 90,201)( 91,200)( 92,199)( 93,198)( 94,197)( 95,196)( 96,195)( 97,194)( 98,193)( 99,192)(100,191)(101,190)(102,189);; s2 := ( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)( 18, 36)( 19, 35)( 20, 51)( 21, 50)( 22, 49)( 23, 48)( 24, 47)( 25, 46)( 26, 45)( 27, 44)( 28, 43)( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)( 60, 62)( 69, 87)( 70, 86)( 71,102)( 72,101)( 73,100)( 74, 99)( 75, 98)( 76, 97)( 77, 96)( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)(111,113)(120,138)(121,137)(122,153)(123,152)(124,151)(125,150)(126,149)(127,148)(128,147)(129,146)(130,145)(131,144)(132,143)(133,142)(134,141)(135,140)(136,139)(154,155)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)(171,189)(172,188)(173,204)(174,203)(175,202)(176,201)(177,200)(178,199)(179,198)(180,197)(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190);; s3 := ( 1, 18)( 2, 19)( 3, 20)( 4, 21)( 5, 22)( 6, 23)( 7, 24)( 8, 25)( 9, 26)( 10, 27)( 11, 28)( 12, 29)( 13, 30)( 14, 31)( 15, 32)( 16, 33)( 17, 34)( 52, 69)( 53, 70)( 54, 71)( 55, 72)( 56, 73)( 57, 74)( 58, 75)( 59, 76)( 60, 77)( 61, 78)( 62, 79)( 63, 80)( 64, 81)( 65, 82)( 66, 83)( 67, 84)( 68, 85)(103,120)(104,121)(105,122)(106,123)(107,124)(108,125)(109,126)(110,127)(111,128)(112,129)(113,130)(114,131)(115,132)(116,133)(117,134)(118,135)(119,136)(154,171)(155,172)(156,173)(157,174)(158,175)(159,176)(160,177)(161,178)(162,179)(163,180)(164,181)(165,182)(166,183)(167,184)(168,185)(169,186)(170,187);; 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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(204)!(103,154)(104,155)(105,156)(106,157)(107,158)(108,159)(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)(117,168)(118,169)(119,170)(120,171)(121,172)(122,173)(123,174)(124,175)(125,176)(126,177)(127,178)(128,179)(129,180)(130,181)(131,182)(132,183)(133,184)(134,185)(135,186)(136,187)(137,188)(138,189)(139,190)(140,191)(141,192)(142,193)(143,194)(144,195)(145,196)(146,197)(147,198)(148,199)(149,200)(150,201)(151,202)(152,203)(153,204); s1 := Sym(204)!( 1,103)( 2,119)( 3,118)( 4,117)( 5,116)( 6,115)( 7,114)( 8,113)( 9,112)( 10,111)( 11,110)( 12,109)( 13,108)( 14,107)( 15,106)( 16,105)( 17,104)( 18,120)( 19,136)( 20,135)( 21,134)( 22,133)( 23,132)( 24,131)( 25,130)( 26,129)( 27,128)( 28,127)( 29,126)( 30,125)( 31,124)( 32,123)( 33,122)( 34,121)( 35,137)( 36,153)( 37,152)( 38,151)( 39,150)( 40,149)( 41,148)( 42,147)( 43,146)( 44,145)( 45,144)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,154)( 53,170)( 54,169)( 55,168)( 56,167)( 57,166)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)( 64,159)( 65,158)( 66,157)( 67,156)( 68,155)( 69,171)( 70,187)( 71,186)( 72,185)( 73,184)( 74,183)( 75,182)( 76,181)( 77,180)( 78,179)( 79,178)( 80,177)( 81,176)( 82,175)( 83,174)( 84,173)( 85,172)( 86,188)( 87,204)( 88,203)( 89,202)( 90,201)( 91,200)( 92,199)( 93,198)( 94,197)( 95,196)( 96,195)( 97,194)( 98,193)( 99,192)(100,191)(101,190)(102,189); s2 := Sym(204)!( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)( 18, 36)( 19, 35)( 20, 51)( 21, 50)( 22, 49)( 23, 48)( 24, 47)( 25, 46)( 26, 45)( 27, 44)( 28, 43)( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)( 60, 62)( 69, 87)( 70, 86)( 71,102)( 72,101)( 73,100)( 74, 99)( 75, 98)( 76, 97)( 77, 96)( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)(111,113)(120,138)(121,137)(122,153)(123,152)(124,151)(125,150)(126,149)(127,148)(128,147)(129,146)(130,145)(131,144)(132,143)(133,142)(134,141)(135,140)(136,139)(154,155)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)(171,189)(172,188)(173,204)(174,203)(175,202)(176,201)(177,200)(178,199)(179,198)(180,197)(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190); s3 := Sym(204)!( 1, 18)( 2, 19)( 3, 20)( 4, 21)( 5, 22)( 6, 23)( 7, 24)( 8, 25)( 9, 26)( 10, 27)( 11, 28)( 12, 29)( 13, 30)( 14, 31)( 15, 32)( 16, 33)( 17, 34)( 52, 69)( 53, 70)( 54, 71)( 55, 72)( 56, 73)( 57, 74)( 58, 75)( 59, 76)( 60, 77)( 61, 78)( 62, 79)( 63, 80)( 64, 81)( 65, 82)( 66, 83)( 67, 84)( 68, 85)(103,120)(104,121)(105,122)(106,123)(107,124)(108,125)(109,126)(110,127)(111,128)(112,129)(113,130)(114,131)(115,132)(116,133)(117,134)(118,135)(119,136)(154,171)(155,172)(156,173)(157,174)(158,175)(159,176)(160,177)(161,178)(162,179)(163,180)(164,181)(165,182)(166,183)(167,184)(168,185)(169,186)(170,187); poly := sub<Sym(204)|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, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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.