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: {{4,20|2},{20,10|2}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

{2,10,10}*400a

5-fold

10-fold

20-fold

25-fold

{4,4,2}*64

40-fold

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

References