Polytope of Type {10,4,3} with group SmallGroup(480,1193)

Overview

Group: SmallGroup(480,1193)
Rank: 4
Schläfli Type: {10,4,3}
Vertices, edges, …: 10, 40, 12, 6
Order of s₀s₁s₂s₃: 30
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{10,4|2},{4,3}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

4-fold

{10,2,3}*120

5-fold

{2,4,3}*96

8-fold

{5,2,3}*60

10-fold

{2,4,3}*48

20-fold

{2,2,3}*24

Covers minimal covers in bold

2-fold

3-fold

4-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s1*s3*s2*s1*s2*s3> of order 2

4 facets

2 of {10,4}*80
2 of {10,2}*40

10 vertex figures

10 of 2-fold non-regular quotient of {4,3}*48

Representations

Permutation Representation (GAP)

s0 := (  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)( 12, 16)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)(112,116);;
s1 := (  1, 67)(  2, 68)(  3, 65)(  4, 66)(  5, 63)(  6, 64)(  7, 61)(  8, 62)(  9, 79)( 10, 80)( 11, 77)( 12, 78)( 13, 75)( 14, 76)( 15, 73)( 16, 74)( 17, 71)( 18, 72)( 19, 69)( 20, 70)( 21, 87)( 22, 88)( 23, 85)( 24, 86)( 25, 83)( 26, 84)( 27, 81)( 28, 82)( 29, 99)( 30,100)( 31, 97)( 32, 98)( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 91)( 38, 92)( 39, 89)( 40, 90)( 41,107)( 42,108)( 43,105)( 44,106)( 45,103)( 46,104)( 47,101)( 48,102)( 49,119)( 50,120)( 51,117)( 52,118)( 53,115)( 54,116)( 55,113)( 56,114)( 57,111)( 58,112)( 59,109)( 60,110);;
s2 := (  2,  3)(  6,  7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)( 31, 50)( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)( 39, 58)( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)( 82,103)( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)( 90,111)( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)( 98,119)( 99,118)(100,120);;
s3 := (  1, 41)(  2, 44)(  3, 43)(  4, 42)(  5, 45)(  6, 48)(  7, 47)(  8, 46)(  9, 49)( 10, 52)( 11, 51)( 12, 50)( 13, 53)( 14, 56)( 15, 55)( 16, 54)( 17, 57)( 18, 60)( 19, 59)( 20, 58)( 22, 24)( 26, 28)( 30, 32)( 34, 36)( 38, 40)( 61,101)( 62,104)( 63,103)( 64,102)( 65,105)( 66,108)( 67,107)( 68,106)( 69,109)( 70,112)( 71,111)( 72,110)( 73,113)( 74,116)( 75,115)( 76,114)( 77,117)( 78,120)( 79,119)( 80,118)( 82, 84)( 86, 88)( 90, 92)( 94, 96)( 98,100);;
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, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
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(120)!(  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)( 12, 16)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)(112,116);
s1 := Sym(120)!(  1, 67)(  2, 68)(  3, 65)(  4, 66)(  5, 63)(  6, 64)(  7, 61)(  8, 62)(  9, 79)( 10, 80)( 11, 77)( 12, 78)( 13, 75)( 14, 76)( 15, 73)( 16, 74)( 17, 71)( 18, 72)( 19, 69)( 20, 70)( 21, 87)( 22, 88)( 23, 85)( 24, 86)( 25, 83)( 26, 84)( 27, 81)( 28, 82)( 29, 99)( 30,100)( 31, 97)( 32, 98)( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 91)( 38, 92)( 39, 89)( 40, 90)( 41,107)( 42,108)( 43,105)( 44,106)( 45,103)( 46,104)( 47,101)( 48,102)( 49,119)( 50,120)( 51,117)( 52,118)( 53,115)( 54,116)( 55,113)( 56,114)( 57,111)( 58,112)( 59,109)( 60,110);
s2 := Sym(120)!(  2,  3)(  6,  7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)( 31, 50)( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)( 39, 58)( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)( 82,103)( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)( 90,111)( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)( 98,119)( 99,118)(100,120);
s3 := Sym(120)!(  1, 41)(  2, 44)(  3, 43)(  4, 42)(  5, 45)(  6, 48)(  7, 47)(  8, 46)(  9, 49)( 10, 52)( 11, 51)( 12, 50)( 13, 53)( 14, 56)( 15, 55)( 16, 54)( 17, 57)( 18, 60)( 19, 59)( 20, 58)( 22, 24)( 26, 28)( 30, 32)( 34, 36)( 38, 40)( 61,101)( 62,104)( 63,103)( 64,102)( 65,105)( 66,108)( 67,107)( 68,106)( 69,109)( 70,112)( 71,111)( 72,110)( 73,113)( 74,116)( 75,115)( 76,114)( 77,117)( 78,120)( 79,119)( 80,118)( 82, 84)( 86, 88)( 90, 92)( 94, 96)( 98,100);
poly := sub<Sym(120)|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, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, 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.