Polytope of Type {4,20,10} with group SmallGroup(1600,7723)

Overview

Group: SmallGroup(1600,7723)
Rank: 4
Schläfli Type: {4,20,10}
Vertices, edges, …: 4, 40, 100, 10
Order of s₀s₁s₂s₃: 20
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

{2,10,10}*400c

5-fold

{4,20,2}*320

8-fold

{2,5,10}*200

10-fold

20-fold

{2,10,2}*80

25-fold

{4,4,2}*64

40-fold

{2,5,2}*40

50-fold

100-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 := (101,151)(102,152)(103,153)(104,154)(105,155)(106,156)(107,157)(108,158)(109,159)(110,160)(111,161)(112,162)(113,163)(114,164)(115,165)(116,166)(117,167)(118,168)(119,169)(120,170)(121,171)(122,172)(123,173)(124,174)(125,175)(126,176)(127,177)(128,178)(129,179)(130,180)(131,181)(132,182)(133,183)(134,184)(135,185)(136,186)(137,187)(138,188)(139,189)(140,190)(141,191)(142,192)(143,193)(144,194)(145,195)(146,196)(147,197)(148,198)(149,199)(150,200);;
s1 := (  1,101)(  2,105)(  3,104)(  4,103)(  5,102)(  6,121)(  7,125)(  8,124)(  9,123)( 10,122)( 11,116)( 12,120)( 13,119)( 14,118)( 15,117)( 16,111)( 17,115)( 18,114)( 19,113)( 20,112)( 21,106)( 22,110)( 23,109)( 24,108)( 25,107)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,146)( 32,150)( 33,149)( 34,148)( 35,147)( 36,141)( 37,145)( 38,144)( 39,143)( 40,142)( 41,136)( 42,140)( 43,139)( 44,138)( 45,137)( 46,131)( 47,135)( 48,134)( 49,133)( 50,132)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)( 56,171)( 57,175)( 58,174)( 59,173)( 60,172)( 61,166)( 62,170)( 63,169)( 64,168)( 65,167)( 66,161)( 67,165)( 68,164)( 69,163)( 70,162)( 71,156)( 72,160)( 73,159)( 74,158)( 75,157)( 76,176)( 77,180)( 78,179)( 79,178)( 80,177)( 81,196)( 82,200)( 83,199)( 84,198)( 85,197)( 86,191)( 87,195)( 88,194)( 89,193)( 90,192)( 91,186)( 92,190)( 93,189)( 94,188)( 95,187)( 96,181)( 97,185)( 98,184)( 99,183)(100,182);;
s2 := (  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 22)( 12, 21)( 13, 25)( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 32)( 27, 31)( 28, 35)( 29, 34)( 30, 33)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)( 43, 45)( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 82)( 77, 81)( 78, 85)( 79, 84)( 80, 83)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)( 93, 95)(101,132)(102,131)(103,135)(104,134)(105,133)(106,127)(107,126)(108,130)(109,129)(110,128)(111,147)(112,146)(113,150)(114,149)(115,148)(116,142)(117,141)(118,145)(119,144)(120,143)(121,137)(122,136)(123,140)(124,139)(125,138)(151,182)(152,181)(153,185)(154,184)(155,183)(156,177)(157,176)(158,180)(159,179)(160,178)(161,197)(162,196)(163,200)(164,199)(165,198)(166,192)(167,191)(168,195)(169,194)(170,193)(171,187)(172,186)(173,190)(174,189)(175,188);;
s3 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)(190,195);;
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*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*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(200)!(101,151)(102,152)(103,153)(104,154)(105,155)(106,156)(107,157)(108,158)(109,159)(110,160)(111,161)(112,162)(113,163)(114,164)(115,165)(116,166)(117,167)(118,168)(119,169)(120,170)(121,171)(122,172)(123,173)(124,174)(125,175)(126,176)(127,177)(128,178)(129,179)(130,180)(131,181)(132,182)(133,183)(134,184)(135,185)(136,186)(137,187)(138,188)(139,189)(140,190)(141,191)(142,192)(143,193)(144,194)(145,195)(146,196)(147,197)(148,198)(149,199)(150,200);
s1 := Sym(200)!(  1,101)(  2,105)(  3,104)(  4,103)(  5,102)(  6,121)(  7,125)(  8,124)(  9,123)( 10,122)( 11,116)( 12,120)( 13,119)( 14,118)( 15,117)( 16,111)( 17,115)( 18,114)( 19,113)( 20,112)( 21,106)( 22,110)( 23,109)( 24,108)( 25,107)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,146)( 32,150)( 33,149)( 34,148)( 35,147)( 36,141)( 37,145)( 38,144)( 39,143)( 40,142)( 41,136)( 42,140)( 43,139)( 44,138)( 45,137)( 46,131)( 47,135)( 48,134)( 49,133)( 50,132)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)( 56,171)( 57,175)( 58,174)( 59,173)( 60,172)( 61,166)( 62,170)( 63,169)( 64,168)( 65,167)( 66,161)( 67,165)( 68,164)( 69,163)( 70,162)( 71,156)( 72,160)( 73,159)( 74,158)( 75,157)( 76,176)( 77,180)( 78,179)( 79,178)( 80,177)( 81,196)( 82,200)( 83,199)( 84,198)( 85,197)( 86,191)( 87,195)( 88,194)( 89,193)( 90,192)( 91,186)( 92,190)( 93,189)( 94,188)( 95,187)( 96,181)( 97,185)( 98,184)( 99,183)(100,182);
s2 := Sym(200)!(  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 22)( 12, 21)( 13, 25)( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 32)( 27, 31)( 28, 35)( 29, 34)( 30, 33)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)( 43, 45)( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 82)( 77, 81)( 78, 85)( 79, 84)( 80, 83)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)( 93, 95)(101,132)(102,131)(103,135)(104,134)(105,133)(106,127)(107,126)(108,130)(109,129)(110,128)(111,147)(112,146)(113,150)(114,149)(115,148)(116,142)(117,141)(118,145)(119,144)(120,143)(121,137)(122,136)(123,140)(124,139)(125,138)(151,182)(152,181)(153,185)(154,184)(155,183)(156,177)(157,176)(158,180)(159,179)(160,178)(161,197)(162,196)(163,200)(164,199)(165,198)(166,192)(167,191)(168,195)(169,194)(170,193)(171,187)(172,186)(173,190)(174,189)(175,188);
s3 := Sym(200)!(  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)(190,195);
poly := sub<Sym(200)|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, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References