Overview
- Group
- SmallGroup(1728,46116)
- Rank
- 6
- Schläfli Type
- {2,6,6,3,4}
- Vertices, edges, …
- 2, 6, 18, 9, 6, 4
- Order of s0s1s2s3s4s5
- 6
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
9-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 7, 11)( 8, 12)( 9, 13)( 10, 14)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 31)( 24, 32)( 25, 33)( 26, 34)( 43, 47)( 44, 48)( 45, 49)( 46, 50)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 71)( 56, 72)( 57, 73)( 58, 74)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 79, 83)( 80, 84)( 81, 85)( 82, 86)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,107)( 92,108)( 93,109)( 94,110)( 95,103)( 96,104)( 97,105)( 98,106)(115,119)(116,120)(117,121)(118,122)(123,135)(124,136)(125,137)(126,138)(127,143)(128,144)(129,145)(130,146)(131,139)(132,140)(133,141)(134,142)(151,155)(152,156)(153,157)(154,158)(159,171)(160,172)(161,173)(162,174)(163,179)(164,180)(165,181)(166,182)(167,175)(168,176)(169,177)(170,178)(187,191)(188,192)(189,193)(190,194)(195,207)(196,208)(197,209)(198,210)(199,215)(200,216)(201,217)(202,218)(203,211)(204,212)(205,213)(206,214);; s2 := ( 3,123)( 4,124)( 5,125)( 6,126)( 7,131)( 8,132)( 9,133)( 10,134)( 11,127)( 12,128)( 13,129)( 14,130)( 15,111)( 16,112)( 17,113)( 18,114)( 19,119)( 20,120)( 21,121)( 22,122)( 23,115)( 24,116)( 25,117)( 26,118)( 27,135)( 28,136)( 29,137)( 30,138)( 31,143)( 32,144)( 33,145)( 34,146)( 35,139)( 36,140)( 37,141)( 38,142)( 39,159)( 40,160)( 41,161)( 42,162)( 43,167)( 44,168)( 45,169)( 46,170)( 47,163)( 48,164)( 49,165)( 50,166)( 51,147)( 52,148)( 53,149)( 54,150)( 55,155)( 56,156)( 57,157)( 58,158)( 59,151)( 60,152)( 61,153)( 62,154)( 63,171)( 64,172)( 65,173)( 66,174)( 67,179)( 68,180)( 69,181)( 70,182)( 71,175)( 72,176)( 73,177)( 74,178)( 75,195)( 76,196)( 77,197)( 78,198)( 79,203)( 80,204)( 81,205)( 82,206)( 83,199)( 84,200)( 85,201)( 86,202)( 87,183)( 88,184)( 89,185)( 90,186)( 91,191)( 92,192)( 93,193)( 94,194)( 95,187)( 96,188)( 97,189)( 98,190)( 99,207)(100,208)(101,209)(102,210)(103,215)(104,216)(105,217)(106,218)(107,211)(108,212)(109,213)(110,214);; s3 := ( 3, 39)( 4, 40)( 5, 42)( 6, 41)( 7, 47)( 8, 48)( 9, 50)( 10, 49)( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 55)( 16, 56)( 17, 58)( 18, 57)( 19, 51)( 20, 52)( 21, 54)( 22, 53)( 23, 59)( 24, 60)( 25, 62)( 26, 61)( 27, 71)( 28, 72)( 29, 74)( 30, 73)( 31, 67)( 32, 68)( 33, 70)( 34, 69)( 35, 63)( 36, 64)( 37, 66)( 38, 65)( 77, 78)( 79, 83)( 80, 84)( 81, 86)( 82, 85)( 87, 91)( 88, 92)( 89, 94)( 90, 93)( 97, 98)( 99,107)(100,108)(101,110)(102,109)(105,106)(111,147)(112,148)(113,150)(114,149)(115,155)(116,156)(117,158)(118,157)(119,151)(120,152)(121,154)(122,153)(123,163)(124,164)(125,166)(126,165)(127,159)(128,160)(129,162)(130,161)(131,167)(132,168)(133,170)(134,169)(135,179)(136,180)(137,182)(138,181)(139,175)(140,176)(141,178)(142,177)(143,171)(144,172)(145,174)(146,173)(185,186)(187,191)(188,192)(189,194)(190,193)(195,199)(196,200)(197,202)(198,201)(205,206)(207,215)(208,216)(209,218)(210,217)(213,214);; s4 := ( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 23)( 20, 25)( 21, 24)( 22, 26)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 39, 75)( 40, 77)( 41, 76)( 42, 78)( 43, 83)( 44, 85)( 45, 84)( 46, 86)( 47, 79)( 48, 81)( 49, 80)( 50, 82)( 51, 87)( 52, 89)( 53, 88)( 54, 90)( 55, 95)( 56, 97)( 57, 96)( 58, 98)( 59, 91)( 60, 93)( 61, 92)( 62, 94)( 63, 99)( 64,101)( 65,100)( 66,102)( 67,107)( 68,109)( 69,108)( 70,110)( 71,103)( 72,105)( 73,104)( 74,106)(112,113)(115,119)(116,121)(117,120)(118,122)(124,125)(127,131)(128,133)(129,132)(130,134)(136,137)(139,143)(140,145)(141,144)(142,146)(147,183)(148,185)(149,184)(150,186)(151,191)(152,193)(153,192)(154,194)(155,187)(156,189)(157,188)(158,190)(159,195)(160,197)(161,196)(162,198)(163,203)(164,205)(165,204)(166,206)(167,199)(168,201)(169,200)(170,202)(171,207)(172,209)(173,208)(174,210)(175,215)(176,217)(177,216)(178,218)(179,211)(180,213)(181,212)(182,214);; s5 := ( 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)(209,210)(211,212)(213,214)(215,216)(217,218);; 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, 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, s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5, s3*s5*s4*s3*s5*s4*s3*s5*s4,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(218)!(1,2); s1 := Sym(218)!( 7, 11)( 8, 12)( 9, 13)( 10, 14)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 31)( 24, 32)( 25, 33)( 26, 34)( 43, 47)( 44, 48)( 45, 49)( 46, 50)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 71)( 56, 72)( 57, 73)( 58, 74)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 79, 83)( 80, 84)( 81, 85)( 82, 86)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,107)( 92,108)( 93,109)( 94,110)( 95,103)( 96,104)( 97,105)( 98,106)(115,119)(116,120)(117,121)(118,122)(123,135)(124,136)(125,137)(126,138)(127,143)(128,144)(129,145)(130,146)(131,139)(132,140)(133,141)(134,142)(151,155)(152,156)(153,157)(154,158)(159,171)(160,172)(161,173)(162,174)(163,179)(164,180)(165,181)(166,182)(167,175)(168,176)(169,177)(170,178)(187,191)(188,192)(189,193)(190,194)(195,207)(196,208)(197,209)(198,210)(199,215)(200,216)(201,217)(202,218)(203,211)(204,212)(205,213)(206,214); s2 := Sym(218)!( 3,123)( 4,124)( 5,125)( 6,126)( 7,131)( 8,132)( 9,133)( 10,134)( 11,127)( 12,128)( 13,129)( 14,130)( 15,111)( 16,112)( 17,113)( 18,114)( 19,119)( 20,120)( 21,121)( 22,122)( 23,115)( 24,116)( 25,117)( 26,118)( 27,135)( 28,136)( 29,137)( 30,138)( 31,143)( 32,144)( 33,145)( 34,146)( 35,139)( 36,140)( 37,141)( 38,142)( 39,159)( 40,160)( 41,161)( 42,162)( 43,167)( 44,168)( 45,169)( 46,170)( 47,163)( 48,164)( 49,165)( 50,166)( 51,147)( 52,148)( 53,149)( 54,150)( 55,155)( 56,156)( 57,157)( 58,158)( 59,151)( 60,152)( 61,153)( 62,154)( 63,171)( 64,172)( 65,173)( 66,174)( 67,179)( 68,180)( 69,181)( 70,182)( 71,175)( 72,176)( 73,177)( 74,178)( 75,195)( 76,196)( 77,197)( 78,198)( 79,203)( 80,204)( 81,205)( 82,206)( 83,199)( 84,200)( 85,201)( 86,202)( 87,183)( 88,184)( 89,185)( 90,186)( 91,191)( 92,192)( 93,193)( 94,194)( 95,187)( 96,188)( 97,189)( 98,190)( 99,207)(100,208)(101,209)(102,210)(103,215)(104,216)(105,217)(106,218)(107,211)(108,212)(109,213)(110,214); s3 := Sym(218)!( 3, 39)( 4, 40)( 5, 42)( 6, 41)( 7, 47)( 8, 48)( 9, 50)( 10, 49)( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 55)( 16, 56)( 17, 58)( 18, 57)( 19, 51)( 20, 52)( 21, 54)( 22, 53)( 23, 59)( 24, 60)( 25, 62)( 26, 61)( 27, 71)( 28, 72)( 29, 74)( 30, 73)( 31, 67)( 32, 68)( 33, 70)( 34, 69)( 35, 63)( 36, 64)( 37, 66)( 38, 65)( 77, 78)( 79, 83)( 80, 84)( 81, 86)( 82, 85)( 87, 91)( 88, 92)( 89, 94)( 90, 93)( 97, 98)( 99,107)(100,108)(101,110)(102,109)(105,106)(111,147)(112,148)(113,150)(114,149)(115,155)(116,156)(117,158)(118,157)(119,151)(120,152)(121,154)(122,153)(123,163)(124,164)(125,166)(126,165)(127,159)(128,160)(129,162)(130,161)(131,167)(132,168)(133,170)(134,169)(135,179)(136,180)(137,182)(138,181)(139,175)(140,176)(141,178)(142,177)(143,171)(144,172)(145,174)(146,173)(185,186)(187,191)(188,192)(189,194)(190,193)(195,199)(196,200)(197,202)(198,201)(205,206)(207,215)(208,216)(209,218)(210,217)(213,214); s4 := Sym(218)!( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 23)( 20, 25)( 21, 24)( 22, 26)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 39, 75)( 40, 77)( 41, 76)( 42, 78)( 43, 83)( 44, 85)( 45, 84)( 46, 86)( 47, 79)( 48, 81)( 49, 80)( 50, 82)( 51, 87)( 52, 89)( 53, 88)( 54, 90)( 55, 95)( 56, 97)( 57, 96)( 58, 98)( 59, 91)( 60, 93)( 61, 92)( 62, 94)( 63, 99)( 64,101)( 65,100)( 66,102)( 67,107)( 68,109)( 69,108)( 70,110)( 71,103)( 72,105)( 73,104)( 74,106)(112,113)(115,119)(116,121)(117,120)(118,122)(124,125)(127,131)(128,133)(129,132)(130,134)(136,137)(139,143)(140,145)(141,144)(142,146)(147,183)(148,185)(149,184)(150,186)(151,191)(152,193)(153,192)(154,194)(155,187)(156,189)(157,188)(158,190)(159,195)(160,197)(161,196)(162,198)(163,203)(164,205)(165,204)(166,206)(167,199)(168,201)(169,200)(170,202)(171,207)(172,209)(173,208)(174,210)(175,215)(176,217)(177,216)(178,218)(179,211)(180,213)(181,212)(182,214); s5 := Sym(218)!( 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)(209,210)(211,212)(213,214)(215,216)(217,218); poly := sub<Sym(218)|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, 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, s3*s4*s3*s4*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5, s3*s5*s4*s3*s5*s4*s3*s5*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;