Polytope of Type {30,3} with group SmallGroup(1500,37)

Overview

Group: SmallGroup(1500,37)
Rank: 3
Schläfli Type: {30,3}
Vertices, edges, …: 250, 375, 25
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 30
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

5-fold

{6,3}*300

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=<(s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 5

5 facets

5 of {30}*60

50 vertex figures

50 of {3}*6

Representations

Permutation Representation (GAP)

s0 := (  2,  5)(  3,  4)(  6, 35)(  7, 34)(  8, 33)(  9, 32)( 10, 31)( 11, 61)( 12, 65)( 13, 64)( 14, 63)( 15, 62)( 16, 94)( 17, 93)( 18, 92)( 19, 91)( 20, 95)( 21,124)( 22,123)( 23,122)( 24,121)( 25,125)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 37, 40)( 38, 39)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 70)( 46, 99)( 47, 98)( 48, 97)( 49, 96)( 50,100)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56,110)( 57,109)( 58,108)( 59,107)( 60,106)( 71, 74)( 72, 73)( 81, 85)( 82, 84)( 86,111)( 87,115)( 88,114)( 89,113)( 90,112)(116,119)(117,118);;
s1 := (  1, 11)(  2, 15)(  3, 14)(  4, 13)(  5, 12)(  7, 10)(  8,  9)( 16, 21)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 51, 67)( 52, 66)( 53, 70)( 54, 69)( 55, 68)( 56, 62)( 57, 61)( 58, 65)( 59, 64)( 60, 63)( 71, 72)( 73, 75)( 76, 84)( 77, 83)( 78, 82)( 79, 81)( 80, 85)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90,100)( 91, 94)( 92, 93)(101,122)(102,121)(103,125)(104,124)(105,123)(106,117)(107,116)(108,120)(109,119)(110,118)(111,112)(113,115);;
s2 := (  2,  5)(  3,  4)(  6,122)(  7,121)(  8,125)(  9,124)( 10,123)( 11, 95)( 12, 94)( 13, 93)( 14, 92)( 15, 91)( 16, 65)( 17, 64)( 18, 63)( 19, 62)( 20, 61)( 21, 32)( 22, 31)( 23, 35)( 24, 34)( 25, 33)( 27, 30)( 28, 29)( 36,120)( 37,119)( 38,118)( 39,117)( 40,116)( 41, 90)( 42, 89)( 43, 88)( 44, 87)( 45, 86)( 46, 57)( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 52, 55)( 53, 54)( 66,115)( 67,114)( 68,113)( 69,112)( 70,111)( 71, 82)( 72, 81)( 73, 85)( 74, 84)( 75, 83)( 77, 80)( 78, 79)( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(102,105)(103,104);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(125)!(  2,  5)(  3,  4)(  6, 35)(  7, 34)(  8, 33)(  9, 32)( 10, 31)( 11, 61)( 12, 65)( 13, 64)( 14, 63)( 15, 62)( 16, 94)( 17, 93)( 18, 92)( 19, 91)( 20, 95)( 21,124)( 22,123)( 23,122)( 24,121)( 25,125)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 37, 40)( 38, 39)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 70)( 46, 99)( 47, 98)( 48, 97)( 49, 96)( 50,100)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56,110)( 57,109)( 58,108)( 59,107)( 60,106)( 71, 74)( 72, 73)( 81, 85)( 82, 84)( 86,111)( 87,115)( 88,114)( 89,113)( 90,112)(116,119)(117,118);
s1 := Sym(125)!(  1, 11)(  2, 15)(  3, 14)(  4, 13)(  5, 12)(  7, 10)(  8,  9)( 16, 21)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 51, 67)( 52, 66)( 53, 70)( 54, 69)( 55, 68)( 56, 62)( 57, 61)( 58, 65)( 59, 64)( 60, 63)( 71, 72)( 73, 75)( 76, 84)( 77, 83)( 78, 82)( 79, 81)( 80, 85)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90,100)( 91, 94)( 92, 93)(101,122)(102,121)(103,125)(104,124)(105,123)(106,117)(107,116)(108,120)(109,119)(110,118)(111,112)(113,115);
s2 := Sym(125)!(  2,  5)(  3,  4)(  6,122)(  7,121)(  8,125)(  9,124)( 10,123)( 11, 95)( 12, 94)( 13, 93)( 14, 92)( 15, 91)( 16, 65)( 17, 64)( 18, 63)( 19, 62)( 20, 61)( 21, 32)( 22, 31)( 23, 35)( 24, 34)( 25, 33)( 27, 30)( 28, 29)( 36,120)( 37,119)( 38,118)( 39,117)( 40,116)( 41, 90)( 42, 89)( 43, 88)( 44, 87)( 45, 86)( 46, 57)( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 52, 55)( 53, 54)( 66,115)( 67,114)( 68,113)( 69,112)( 70,111)( 71, 82)( 72, 81)( 73, 85)( 74, 84)( 75, 83)( 77, 80)( 78, 79)( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(102,105)(103,104);
poly := sub<Sym(125)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.