Polytope of Type {4,4,20} with group SmallGroup(1280,201148)

Overview

Group: SmallGroup(1280,201148)
Rank: 4
Schläfli Type: {4,4,20}
Vertices, edges, …: 8, 16, 80, 20
Order of s₀s₁s₂s₃: 20
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{4,4}₄,{4,20|2}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

5-fold

{4,4,4}*256b

8-fold

10-fold

16-fold

20-fold

32-fold

{2,2,5}*40

40-fold

80-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s1*s2)^2> of order 2

20 facets

20 of 2-fold non-regular quotient of {4,4}*64

6 vertex figures

4 of {2,20}*80
2 of {4,20}*160

P/N, where N=<(s0*s1)^2> of order 2

20 facets

20 of 2-fold non-regular quotient of {4,4}*64

4 vertex figures

4 of {4,20}*160

Representations

Permutation Representation (GAP)

s0 := (  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, 66)( 22, 67)( 23, 68)( 24, 69)( 25, 70)( 26, 61)( 27, 62)( 28, 63)( 29, 64)( 30, 65)( 31, 76)( 32, 77)( 33, 78)( 34, 79)( 35, 80)( 36, 71)( 37, 72)( 38, 73)( 39, 74)( 40, 75)( 81,121)( 82,122)( 83,123)( 84,124)( 85,125)( 86,126)( 87,127)( 88,128)( 89,129)( 90,130)( 91,131)( 92,132)( 93,133)( 94,134)( 95,135)( 96,136)( 97,137)( 98,138)( 99,139)(100,140)(101,146)(102,147)(103,148)(104,149)(105,150)(106,141)(107,142)(108,143)(109,144)(110,145)(111,156)(112,157)(113,158)(114,159)(115,160)(116,151)(117,152)(118,153)(119,154)(120,155);;
s1 := ( 81,101)( 82,102)( 83,103)( 84,104)( 85,105)( 86,106)( 87,107)( 88,108)( 89,109)( 90,110)( 91,111)( 92,112)( 93,113)( 94,114)( 95,115)( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(121,141)(122,142)(123,143)(124,144)(125,145)(126,146)(127,147)(128,148)(129,149)(130,150)(131,151)(132,152)(133,153)(134,154)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160);;
s2 := (  1, 81)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 86)(  7, 90)(  8, 89)(  9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)( 16, 96)( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)( 24,103)( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)( 32,115)( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)( 41,121)( 42,125)( 43,124)( 44,123)( 45,122)( 46,126)( 47,130)( 48,129)( 49,128)( 50,127)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)( 56,136)( 57,140)( 58,139)( 59,138)( 60,137)( 61,141)( 62,145)( 63,144)( 64,143)( 65,142)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,151)( 72,155)( 73,154)( 74,153)( 75,152)( 76,156)( 77,160)( 78,159)( 79,158)( 80,157);;
s3 := (  1, 43)(  2, 42)(  3, 41)(  4, 45)(  5, 44)(  6, 48)(  7, 47)(  8, 46)(  9, 50)( 10, 49)( 11, 53)( 12, 52)( 13, 51)( 14, 55)( 15, 54)( 16, 58)( 17, 57)( 18, 56)( 19, 60)( 20, 59)( 21, 63)( 22, 62)( 23, 61)( 24, 65)( 25, 64)( 26, 68)( 27, 67)( 28, 66)( 29, 70)( 30, 69)( 31, 73)( 32, 72)( 33, 71)( 34, 75)( 35, 74)( 36, 78)( 37, 77)( 38, 76)( 39, 80)( 40, 79)( 81,133)( 82,132)( 83,131)( 84,135)( 85,134)( 86,138)( 87,137)( 88,136)( 89,140)( 90,139)( 91,123)( 92,122)( 93,121)( 94,125)( 95,124)( 96,128)( 97,127)( 98,126)( 99,130)(100,129)(101,153)(102,152)(103,151)(104,155)(105,154)(106,158)(107,157)(108,156)(109,160)(110,159)(111,143)(112,142)(113,141)(114,145)(115,144)(116,148)(117,147)(118,146)(119,150)(120,149);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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(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, 66)( 22, 67)( 23, 68)( 24, 69)( 25, 70)( 26, 61)( 27, 62)( 28, 63)( 29, 64)( 30, 65)( 31, 76)( 32, 77)( 33, 78)( 34, 79)( 35, 80)( 36, 71)( 37, 72)( 38, 73)( 39, 74)( 40, 75)( 81,121)( 82,122)( 83,123)( 84,124)( 85,125)( 86,126)( 87,127)( 88,128)( 89,129)( 90,130)( 91,131)( 92,132)( 93,133)( 94,134)( 95,135)( 96,136)( 97,137)( 98,138)( 99,139)(100,140)(101,146)(102,147)(103,148)(104,149)(105,150)(106,141)(107,142)(108,143)(109,144)(110,145)(111,156)(112,157)(113,158)(114,159)(115,160)(116,151)(117,152)(118,153)(119,154)(120,155);
s1 := Sym(160)!( 81,101)( 82,102)( 83,103)( 84,104)( 85,105)( 86,106)( 87,107)( 88,108)( 89,109)( 90,110)( 91,111)( 92,112)( 93,113)( 94,114)( 95,115)( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(121,141)(122,142)(123,143)(124,144)(125,145)(126,146)(127,147)(128,148)(129,149)(130,150)(131,151)(132,152)(133,153)(134,154)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160);
s2 := Sym(160)!(  1, 81)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 86)(  7, 90)(  8, 89)(  9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)( 16, 96)( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)( 24,103)( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)( 32,115)( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)( 41,121)( 42,125)( 43,124)( 44,123)( 45,122)( 46,126)( 47,130)( 48,129)( 49,128)( 50,127)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)( 56,136)( 57,140)( 58,139)( 59,138)( 60,137)( 61,141)( 62,145)( 63,144)( 64,143)( 65,142)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,151)( 72,155)( 73,154)( 74,153)( 75,152)( 76,156)( 77,160)( 78,159)( 79,158)( 80,157);
s3 := Sym(160)!(  1, 43)(  2, 42)(  3, 41)(  4, 45)(  5, 44)(  6, 48)(  7, 47)(  8, 46)(  9, 50)( 10, 49)( 11, 53)( 12, 52)( 13, 51)( 14, 55)( 15, 54)( 16, 58)( 17, 57)( 18, 56)( 19, 60)( 20, 59)( 21, 63)( 22, 62)( 23, 61)( 24, 65)( 25, 64)( 26, 68)( 27, 67)( 28, 66)( 29, 70)( 30, 69)( 31, 73)( 32, 72)( 33, 71)( 34, 75)( 35, 74)( 36, 78)( 37, 77)( 38, 76)( 39, 80)( 40, 79)( 81,133)( 82,132)( 83,131)( 84,135)( 85,134)( 86,138)( 87,137)( 88,136)( 89,140)( 90,139)( 91,123)( 92,122)( 93,121)( 94,125)( 95,124)( 96,128)( 97,127)( 98,126)( 99,130)(100,129)(101,153)(102,152)(103,151)(104,155)(105,154)(106,158)(107,157)(108,156)(109,160)(110,159)(111,143)(112,142)(113,141)(114,145)(115,144)(116,148)(117,147)(118,146)(119,150)(120,149);
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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.