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Polytope of Type {20,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,4,4}*1280b
if this polytope has a name.
Group : SmallGroup(1280,201151)
Rank : 4
Schlafli Type : {20,4,4}
Number of vertices, edges, etc : 40, 80, 16, 4
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 : {20,4,4}*640, {20,4,2}*640
   4-fold quotients : {20,4,2}*320, {20,2,4}*320, {10,4,4}*320
   5-fold quotients : {4,4,4}*256b
   8-fold quotients : {20,2,2}*160, {10,2,4}*160, {10,4,2}*160
   10-fold quotients : {4,4,4}*128, {4,4,2}*128
   16-fold quotients : {5,2,4}*80, {10,2,2}*80
   20-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   32-fold quotients : {5,2,2}*40
   40-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
   80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 41)(  2, 45)(  3, 44)(  4, 43)(  5, 42)(  6, 46)(  7, 50)(  8, 49)
(  9, 48)( 10, 47)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)( 16, 56)
( 17, 60)( 18, 59)( 19, 58)( 20, 57)( 21, 66)( 22, 70)( 23, 69)( 24, 68)
( 25, 67)( 26, 61)( 27, 65)( 28, 64)( 29, 63)( 30, 62)( 31, 76)( 32, 80)
( 33, 79)( 34, 78)( 35, 77)( 36, 71)( 37, 75)( 38, 74)( 39, 73)( 40, 72)
( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)( 88,129)
( 89,128)( 90,127)( 91,131)( 92,135)( 93,134)( 94,133)( 95,132)( 96,136)
( 97,140)( 98,139)( 99,138)(100,137)(101,146)(102,150)(103,149)(104,148)
(105,147)(106,141)(107,145)(108,144)(109,143)(110,142)(111,156)(112,160)
(113,159)(114,158)(115,157)(116,151)(117,155)(118,154)(119,153)(120,152);;
s1 := (  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 13)( 14, 15)( 16, 18)( 19, 20)
( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 33)( 34, 35)( 36, 38)( 39, 40)
( 41, 43)( 44, 45)( 46, 48)( 49, 50)( 51, 53)( 54, 55)( 56, 58)( 59, 60)
( 61, 63)( 64, 65)( 66, 68)( 69, 70)( 71, 73)( 74, 75)( 76, 78)( 79, 80)
( 81,103)( 82,102)( 83,101)( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)
( 89,110)( 90,109)( 91,113)( 92,112)( 93,111)( 94,115)( 95,114)( 96,118)
( 97,117)( 98,116)( 99,120)(100,119)(121,143)(122,142)(123,141)(124,145)
(125,144)(126,148)(127,147)(128,146)(129,150)(130,149)(131,153)(132,152)
(133,151)(134,155)(135,154)(136,158)(137,157)(138,156)(139,160)(140,159);;
s2 := (  1, 81)(  2, 82)(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)(  8, 88)
(  9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)
( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)( 24,104)
( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)
( 33,113)( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)( 40,120)
( 41,121)( 42,122)( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)( 48,128)
( 49,129)( 50,130)( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)( 56,136)
( 57,137)( 58,138)( 59,139)( 60,140)( 61,141)( 62,142)( 63,143)( 64,144)
( 65,145)( 66,146)( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)( 72,152)
( 73,153)( 74,154)( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)( 80,160);;
s3 := (  1, 41)(  2, 42)(  3, 43)(  4, 44)(  5, 45)(  6, 46)(  7, 47)(  8, 48)
(  9, 49)( 10, 50)( 11, 51)( 12, 52)( 13, 53)( 14, 54)( 15, 55)( 16, 56)
( 17, 57)( 18, 58)( 19, 59)( 20, 60)( 21, 61)( 22, 62)( 23, 63)( 24, 64)
( 25, 65)( 26, 66)( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 71)( 32, 72)
( 33, 73)( 34, 74)( 35, 75)( 36, 76)( 37, 77)( 38, 78)( 39, 79)( 40, 80)
( 81,131)( 82,132)( 83,133)( 84,134)( 85,135)( 86,136)( 87,137)( 88,138)
( 89,139)( 90,140)( 91,121)( 92,122)( 93,123)( 94,124)( 95,125)( 96,126)
( 97,127)( 98,128)( 99,129)(100,130)(101,151)(102,152)(103,153)(104,154)
(105,155)(106,156)(107,157)(108,158)(109,159)(110,160)(111,141)(112,142)
(113,143)(114,144)(115,145)(116,146)(117,147)(118,148)(119,149)(120,150);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(160)!(  1, 41)(  2, 45)(  3, 44)(  4, 43)(  5, 42)(  6, 46)(  7, 50)
(  8, 49)(  9, 48)( 10, 47)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)
( 16, 56)( 17, 60)( 18, 59)( 19, 58)( 20, 57)( 21, 66)( 22, 70)( 23, 69)
( 24, 68)( 25, 67)( 26, 61)( 27, 65)( 28, 64)( 29, 63)( 30, 62)( 31, 76)
( 32, 80)( 33, 79)( 34, 78)( 35, 77)( 36, 71)( 37, 75)( 38, 74)( 39, 73)
( 40, 72)( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)
( 88,129)( 89,128)( 90,127)( 91,131)( 92,135)( 93,134)( 94,133)( 95,132)
( 96,136)( 97,140)( 98,139)( 99,138)(100,137)(101,146)(102,150)(103,149)
(104,148)(105,147)(106,141)(107,145)(108,144)(109,143)(110,142)(111,156)
(112,160)(113,159)(114,158)(115,157)(116,151)(117,155)(118,154)(119,153)
(120,152);
s1 := Sym(160)!(  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 13)( 14, 15)( 16, 18)
( 19, 20)( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 33)( 34, 35)( 36, 38)
( 39, 40)( 41, 43)( 44, 45)( 46, 48)( 49, 50)( 51, 53)( 54, 55)( 56, 58)
( 59, 60)( 61, 63)( 64, 65)( 66, 68)( 69, 70)( 71, 73)( 74, 75)( 76, 78)
( 79, 80)( 81,103)( 82,102)( 83,101)( 84,105)( 85,104)( 86,108)( 87,107)
( 88,106)( 89,110)( 90,109)( 91,113)( 92,112)( 93,111)( 94,115)( 95,114)
( 96,118)( 97,117)( 98,116)( 99,120)(100,119)(121,143)(122,142)(123,141)
(124,145)(125,144)(126,148)(127,147)(128,146)(129,150)(130,149)(131,153)
(132,152)(133,151)(134,155)(135,154)(136,158)(137,157)(138,156)(139,160)
(140,159);
s2 := Sym(160)!(  1, 81)(  2, 82)(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)
(  8, 88)(  9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)
( 16, 96)( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)
( 24,104)( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)
( 32,112)( 33,113)( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)
( 40,120)( 41,121)( 42,122)( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)
( 48,128)( 49,129)( 50,130)( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)
( 56,136)( 57,137)( 58,138)( 59,139)( 60,140)( 61,141)( 62,142)( 63,143)
( 64,144)( 65,145)( 66,146)( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)
( 72,152)( 73,153)( 74,154)( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)
( 80,160);
s3 := Sym(160)!(  1, 41)(  2, 42)(  3, 43)(  4, 44)(  5, 45)(  6, 46)(  7, 47)
(  8, 48)(  9, 49)( 10, 50)( 11, 51)( 12, 52)( 13, 53)( 14, 54)( 15, 55)
( 16, 56)( 17, 57)( 18, 58)( 19, 59)( 20, 60)( 21, 61)( 22, 62)( 23, 63)
( 24, 64)( 25, 65)( 26, 66)( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 71)
( 32, 72)( 33, 73)( 34, 74)( 35, 75)( 36, 76)( 37, 77)( 38, 78)( 39, 79)
( 40, 80)( 81,131)( 82,132)( 83,133)( 84,134)( 85,135)( 86,136)( 87,137)
( 88,138)( 89,139)( 90,140)( 91,121)( 92,122)( 93,123)( 94,124)( 95,125)
( 96,126)( 97,127)( 98,128)( 99,129)(100,130)(101,151)(102,152)(103,153)
(104,154)(105,155)(106,156)(107,157)(108,158)(109,159)(110,160)(111,141)
(112,142)(113,143)(114,144)(115,145)(116,146)(117,147)(118,148)(119,149)
(120,150);
poly := sub<Sym(160)|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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*s0*s1*s0*s1 >; 
 
References : None.
to this polytope