Polytope of Type {20,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,4,10}*1600
Also Known As : {{20,4|2},{4,10|2}}. if this polytope has another name.
Group : SmallGroup(1600,7723)
Rank : 4
Schlafli Type : {20,4,10}
Number of vertices, edges, etc : 20, 40, 20, 10
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {20,2,10}*800, {10,4,10}*800
4-fold quotients : {20,2,5}*400, {10,2,10}*400
5-fold quotients : {20,4,2}*320, {4,4,10}*320
8-fold quotients : {5,2,10}*200, {10,2,5}*200
10-fold quotients : {20,2,2}*160, {2,4,10}*160, {4,2,10}*160, {10,4,2}*160
16-fold quotients : {5,2,5}*100
20-fold quotients : {4,2,5}*80, {2,2,10}*80, {10,2,2}*80
25-fold quotients : {4,4,2}*64
40-fold quotients : {2,2,5}*40, {5,2,2}*40
50-fold quotients : {2,4,2}*32, {4,2,2}*32
100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)
(101,126)(102,130)(103,129)(104,128)(105,127)(106,131)(107,135)(108,134)
(109,133)(110,132)(111,136)(112,140)(113,139)(114,138)(115,137)(116,141)
(117,145)(118,144)(119,143)(120,142)(121,146)(122,150)(123,149)(124,148)
(125,147)(151,176)(152,180)(153,179)(154,178)(155,177)(156,181)(157,185)
(158,184)(159,183)(160,182)(161,186)(162,190)(163,189)(164,188)(165,187)
(166,191)(167,195)(168,194)(169,193)(170,192)(171,196)(172,200)(173,199)
(174,198)(175,197);;
s1 := ( 1,102)( 2,101)( 3,105)( 4,104)( 5,103)( 6,107)( 7,106)( 8,110)
( 9,109)( 10,108)( 11,112)( 12,111)( 13,115)( 14,114)( 15,113)( 16,117)
( 17,116)( 18,120)( 19,119)( 20,118)( 21,122)( 22,121)( 23,125)( 24,124)
( 25,123)( 26,127)( 27,126)( 28,130)( 29,129)( 30,128)( 31,132)( 32,131)
( 33,135)( 34,134)( 35,133)( 36,137)( 37,136)( 38,140)( 39,139)( 40,138)
( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,147)( 47,146)( 48,150)
( 49,149)( 50,148)( 51,152)( 52,151)( 53,155)( 54,154)( 55,153)( 56,157)
( 57,156)( 58,160)( 59,159)( 60,158)( 61,162)( 62,161)( 63,165)( 64,164)
( 65,163)( 66,167)( 67,166)( 68,170)( 69,169)( 70,168)( 71,172)( 72,171)
( 73,175)( 74,174)( 75,173)( 76,177)( 77,176)( 78,180)( 79,179)( 80,178)
( 81,182)( 82,181)( 83,185)( 84,184)( 85,183)( 86,187)( 87,186)( 88,190)
( 89,189)( 90,188)( 91,192)( 92,191)( 93,195)( 94,194)( 95,193)( 96,197)
( 97,196)( 98,200)( 99,199)(100,198);;
s2 := ( 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)
(101,151)(102,152)(103,153)(104,154)(105,155)(106,171)(107,172)(108,173)
(109,174)(110,175)(111,166)(112,167)(113,168)(114,169)(115,170)(116,161)
(117,162)(118,163)(119,164)(120,165)(121,156)(122,157)(123,158)(124,159)
(125,160)(126,176)(127,177)(128,178)(129,179)(130,180)(131,196)(132,197)
(133,198)(134,199)(135,200)(136,191)(137,192)(138,193)(139,194)(140,195)
(141,186)(142,187)(143,188)(144,189)(145,190)(146,181)(147,182)(148,183)
(149,184)(150,185);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, 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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(200)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)
( 98, 99)(101,126)(102,130)(103,129)(104,128)(105,127)(106,131)(107,135)
(108,134)(109,133)(110,132)(111,136)(112,140)(113,139)(114,138)(115,137)
(116,141)(117,145)(118,144)(119,143)(120,142)(121,146)(122,150)(123,149)
(124,148)(125,147)(151,176)(152,180)(153,179)(154,178)(155,177)(156,181)
(157,185)(158,184)(159,183)(160,182)(161,186)(162,190)(163,189)(164,188)
(165,187)(166,191)(167,195)(168,194)(169,193)(170,192)(171,196)(172,200)
(173,199)(174,198)(175,197);
s1 := Sym(200)!( 1,102)( 2,101)( 3,105)( 4,104)( 5,103)( 6,107)( 7,106)
( 8,110)( 9,109)( 10,108)( 11,112)( 12,111)( 13,115)( 14,114)( 15,113)
( 16,117)( 17,116)( 18,120)( 19,119)( 20,118)( 21,122)( 22,121)( 23,125)
( 24,124)( 25,123)( 26,127)( 27,126)( 28,130)( 29,129)( 30,128)( 31,132)
( 32,131)( 33,135)( 34,134)( 35,133)( 36,137)( 37,136)( 38,140)( 39,139)
( 40,138)( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,147)( 47,146)
( 48,150)( 49,149)( 50,148)( 51,152)( 52,151)( 53,155)( 54,154)( 55,153)
( 56,157)( 57,156)( 58,160)( 59,159)( 60,158)( 61,162)( 62,161)( 63,165)
( 64,164)( 65,163)( 66,167)( 67,166)( 68,170)( 69,169)( 70,168)( 71,172)
( 72,171)( 73,175)( 74,174)( 75,173)( 76,177)( 77,176)( 78,180)( 79,179)
( 80,178)( 81,182)( 82,181)( 83,185)( 84,184)( 85,183)( 86,187)( 87,186)
( 88,190)( 89,189)( 90,188)( 91,192)( 92,191)( 93,195)( 94,194)( 95,193)
( 96,197)( 97,196)( 98,200)( 99,199)(100,198);
s2 := 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)(101,151)(102,152)(103,153)(104,154)(105,155)(106,171)(107,172)
(108,173)(109,174)(110,175)(111,166)(112,167)(113,168)(114,169)(115,170)
(116,161)(117,162)(118,163)(119,164)(120,165)(121,156)(122,157)(123,158)
(124,159)(125,160)(126,176)(127,177)(128,178)(129,179)(130,180)(131,196)
(132,197)(133,198)(134,199)(135,200)(136,191)(137,192)(138,193)(139,194)
(140,195)(141,186)(142,187)(143,188)(144,189)(145,190)(146,181)(147,182)
(148,183)(149,184)(150,185);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope