Overview
- Group
- SmallGroup(1760,1190)
- Rank
- 4
- Schläfli Type
- {4,10,22}
- Vertices, edges, …
- 4, 20, 110, 22
- Order of s0s1s2s3
- 220
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{4,10|2},{10,22|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
5-fold
10-fold
11-fold
20-fold
22-fold
44-fold
55-fold
110-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 := (111,166)(112,167)(113,168)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,182)(128,183)(129,184)(130,185)(131,186)(132,187)(133,188)(134,189)(135,190)(136,191)(137,192)(138,193)(139,194)(140,195)(141,196)(142,197)(143,198)(144,199)(145,200)(146,201)(147,202)(148,203)(149,204)(150,205)(151,206)(152,207)(153,208)(154,209)(155,210)(156,211)(157,212)(158,213)(159,214)(160,215)(161,216)(162,217)(163,218)(164,219)(165,220);; s1 := ( 1,111)( 2,112)( 3,113)( 4,114)( 5,115)( 6,116)( 7,117)( 8,118)( 9,119)( 10,120)( 11,121)( 12,155)( 13,156)( 14,157)( 15,158)( 16,159)( 17,160)( 18,161)( 19,162)( 20,163)( 21,164)( 22,165)( 23,144)( 24,145)( 25,146)( 26,147)( 27,148)( 28,149)( 29,150)( 30,151)( 31,152)( 32,153)( 33,154)( 34,133)( 35,134)( 36,135)( 37,136)( 38,137)( 39,138)( 40,139)( 41,140)( 42,141)( 43,142)( 44,143)( 45,122)( 46,123)( 47,124)( 48,125)( 49,126)( 50,127)( 51,128)( 52,129)( 53,130)( 54,131)( 55,132)( 56,166)( 57,167)( 58,168)( 59,169)( 60,170)( 61,171)( 62,172)( 63,173)( 64,174)( 65,175)( 66,176)( 67,210)( 68,211)( 69,212)( 70,213)( 71,214)( 72,215)( 73,216)( 74,217)( 75,218)( 76,219)( 77,220)( 78,199)( 79,200)( 80,201)( 81,202)( 82,203)( 83,204)( 84,205)( 85,206)( 86,207)( 87,208)( 88,209)( 89,188)( 90,189)( 91,190)( 92,191)( 93,192)( 94,193)( 95,194)( 96,195)( 97,196)( 98,197)( 99,198)(100,177)(101,178)(102,179)(103,180)(104,181)(105,182)(106,183)(107,184)(108,185)(109,186)(110,187);; s2 := ( 1, 12)( 2, 22)( 3, 21)( 4, 20)( 5, 19)( 6, 18)( 7, 17)( 8, 16)( 9, 15)( 10, 14)( 11, 13)( 23, 45)( 24, 55)( 25, 54)( 26, 53)( 27, 52)( 28, 51)( 29, 50)( 30, 49)( 31, 48)( 32, 47)( 33, 46)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 56, 67)( 57, 77)( 58, 76)( 59, 75)( 60, 74)( 61, 73)( 62, 72)( 63, 71)( 64, 70)( 65, 69)( 66, 68)( 78,100)( 79,110)( 80,109)( 81,108)( 82,107)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)( 88,101)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(111,122)(112,132)(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)(121,123)(133,155)(134,165)(135,164)(136,163)(137,162)(138,161)(139,160)(140,159)(141,158)(142,157)(143,156)(145,154)(146,153)(147,152)(148,151)(149,150)(166,177)(167,187)(168,186)(169,185)(170,184)(171,183)(172,182)(173,181)(174,180)(175,179)(176,178)(188,210)(189,220)(190,219)(191,218)(192,217)(193,216)(194,215)(195,214)(196,213)(197,212)(198,211)(200,209)(201,208)(202,207)(203,206)(204,205);; s3 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 13)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 46)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 68)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 78, 79)( 80, 88)( 81, 87)( 82, 86)( 83, 85)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)(103,109)(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)(122,123)(124,132)(125,131)(126,130)(127,129)(133,134)(135,143)(136,142)(137,141)(138,140)(144,145)(146,154)(147,153)(148,152)(149,151)(155,156)(157,165)(158,164)(159,163)(160,162)(166,167)(168,176)(169,175)(170,174)(171,173)(177,178)(179,187)(180,186)(181,185)(182,184)(188,189)(190,198)(191,197)(192,196)(193,195)(199,200)(201,209)(202,208)(203,207)(204,206)(210,211)(212,220)(213,219)(214,218)(215,217);; 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(220)!(111,166)(112,167)(113,168)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,182)(128,183)(129,184)(130,185)(131,186)(132,187)(133,188)(134,189)(135,190)(136,191)(137,192)(138,193)(139,194)(140,195)(141,196)(142,197)(143,198)(144,199)(145,200)(146,201)(147,202)(148,203)(149,204)(150,205)(151,206)(152,207)(153,208)(154,209)(155,210)(156,211)(157,212)(158,213)(159,214)(160,215)(161,216)(162,217)(163,218)(164,219)(165,220); s1 := Sym(220)!( 1,111)( 2,112)( 3,113)( 4,114)( 5,115)( 6,116)( 7,117)( 8,118)( 9,119)( 10,120)( 11,121)( 12,155)( 13,156)( 14,157)( 15,158)( 16,159)( 17,160)( 18,161)( 19,162)( 20,163)( 21,164)( 22,165)( 23,144)( 24,145)( 25,146)( 26,147)( 27,148)( 28,149)( 29,150)( 30,151)( 31,152)( 32,153)( 33,154)( 34,133)( 35,134)( 36,135)( 37,136)( 38,137)( 39,138)( 40,139)( 41,140)( 42,141)( 43,142)( 44,143)( 45,122)( 46,123)( 47,124)( 48,125)( 49,126)( 50,127)( 51,128)( 52,129)( 53,130)( 54,131)( 55,132)( 56,166)( 57,167)( 58,168)( 59,169)( 60,170)( 61,171)( 62,172)( 63,173)( 64,174)( 65,175)( 66,176)( 67,210)( 68,211)( 69,212)( 70,213)( 71,214)( 72,215)( 73,216)( 74,217)( 75,218)( 76,219)( 77,220)( 78,199)( 79,200)( 80,201)( 81,202)( 82,203)( 83,204)( 84,205)( 85,206)( 86,207)( 87,208)( 88,209)( 89,188)( 90,189)( 91,190)( 92,191)( 93,192)( 94,193)( 95,194)( 96,195)( 97,196)( 98,197)( 99,198)(100,177)(101,178)(102,179)(103,180)(104,181)(105,182)(106,183)(107,184)(108,185)(109,186)(110,187); s2 := Sym(220)!( 1, 12)( 2, 22)( 3, 21)( 4, 20)( 5, 19)( 6, 18)( 7, 17)( 8, 16)( 9, 15)( 10, 14)( 11, 13)( 23, 45)( 24, 55)( 25, 54)( 26, 53)( 27, 52)( 28, 51)( 29, 50)( 30, 49)( 31, 48)( 32, 47)( 33, 46)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 56, 67)( 57, 77)( 58, 76)( 59, 75)( 60, 74)( 61, 73)( 62, 72)( 63, 71)( 64, 70)( 65, 69)( 66, 68)( 78,100)( 79,110)( 80,109)( 81,108)( 82,107)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)( 88,101)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(111,122)(112,132)(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)(121,123)(133,155)(134,165)(135,164)(136,163)(137,162)(138,161)(139,160)(140,159)(141,158)(142,157)(143,156)(145,154)(146,153)(147,152)(148,151)(149,150)(166,177)(167,187)(168,186)(169,185)(170,184)(171,183)(172,182)(173,181)(174,180)(175,179)(176,178)(188,210)(189,220)(190,219)(191,218)(192,217)(193,216)(194,215)(195,214)(196,213)(197,212)(198,211)(200,209)(201,208)(202,207)(203,206)(204,205); s3 := Sym(220)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 13)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 46)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 68)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 78, 79)( 80, 88)( 81, 87)( 82, 86)( 83, 85)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)(103,109)(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)(122,123)(124,132)(125,131)(126,130)(127,129)(133,134)(135,143)(136,142)(137,141)(138,140)(144,145)(146,154)(147,153)(148,152)(149,151)(155,156)(157,165)(158,164)(159,163)(160,162)(166,167)(168,176)(169,175)(170,174)(171,173)(177,178)(179,187)(180,186)(181,185)(182,184)(188,189)(190,198)(191,197)(192,196)(193,195)(199,200)(201,209)(202,208)(203,207)(204,206)(210,211)(212,220)(213,219)(214,218)(215,217); poly := sub<Sym(220)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.