Overview
- Group
- SmallGroup(600,195)
- Rank
- 3
- Schläfli Type
- {10,30}
- Vertices, edges, …
- 10, 150, 30
- Order of s0s1s2
- 30
- Order of s0s1s2s1
- 10
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
5-fold
6-fold
10-fold
15-fold
25-fold
30-fold
50-fold
75-fold
Covers minimal covers in bold
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 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)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)(137,142)(138,143)(139,144)(140,145);; s1 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 21)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26, 56)( 27, 60)( 28, 59)( 29, 58)( 30, 57)( 31, 51)( 32, 55)( 33, 54)( 34, 53)( 35, 52)( 36, 71)( 37, 75)( 38, 74)( 39, 73)( 40, 72)( 41, 66)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 61)( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 76, 81)( 77, 85)( 78, 84)( 79, 83)( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 92, 95)( 93, 94)(101,131)(102,135)(103,134)(104,133)(105,132)(106,126)(107,130)(108,129)(109,128)(110,127)(111,146)(112,150)(113,149)(114,148)(115,147)(116,141)(117,145)(118,144)(119,143)(120,142)(121,136)(122,140)(123,139)(124,138)(125,137);; s2 := ( 1,102)( 2,101)( 3,105)( 4,104)( 5,103)( 6,122)( 7,121)( 8,125)( 9,124)( 10,123)( 11,117)( 12,116)( 13,120)( 14,119)( 15,118)( 16,112)( 17,111)( 18,115)( 19,114)( 20,113)( 21,107)( 22,106)( 23,110)( 24,109)( 25,108)( 26, 77)( 27, 76)( 28, 80)( 29, 79)( 30, 78)( 31, 97)( 32, 96)( 33,100)( 34, 99)( 35, 98)( 36, 92)( 37, 91)( 38, 95)( 39, 94)( 40, 93)( 41, 87)( 42, 86)( 43, 90)( 44, 89)( 45, 88)( 46, 82)( 47, 81)( 48, 85)( 49, 84)( 50, 83)( 51,127)( 52,126)( 53,130)( 54,129)( 55,128)( 56,147)( 57,146)( 58,150)( 59,149)( 60,148)( 61,142)( 62,141)( 63,145)( 64,144)( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,132)( 72,131)( 73,135)( 74,134)( 75,133);; 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, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(150)!( 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)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)(137,142)(138,143)(139,144)(140,145); s1 := Sym(150)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 21)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26, 56)( 27, 60)( 28, 59)( 29, 58)( 30, 57)( 31, 51)( 32, 55)( 33, 54)( 34, 53)( 35, 52)( 36, 71)( 37, 75)( 38, 74)( 39, 73)( 40, 72)( 41, 66)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 61)( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 76, 81)( 77, 85)( 78, 84)( 79, 83)( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 92, 95)( 93, 94)(101,131)(102,135)(103,134)(104,133)(105,132)(106,126)(107,130)(108,129)(109,128)(110,127)(111,146)(112,150)(113,149)(114,148)(115,147)(116,141)(117,145)(118,144)(119,143)(120,142)(121,136)(122,140)(123,139)(124,138)(125,137); s2 := Sym(150)!( 1,102)( 2,101)( 3,105)( 4,104)( 5,103)( 6,122)( 7,121)( 8,125)( 9,124)( 10,123)( 11,117)( 12,116)( 13,120)( 14,119)( 15,118)( 16,112)( 17,111)( 18,115)( 19,114)( 20,113)( 21,107)( 22,106)( 23,110)( 24,109)( 25,108)( 26, 77)( 27, 76)( 28, 80)( 29, 79)( 30, 78)( 31, 97)( 32, 96)( 33,100)( 34, 99)( 35, 98)( 36, 92)( 37, 91)( 38, 95)( 39, 94)( 40, 93)( 41, 87)( 42, 86)( 43, 90)( 44, 89)( 45, 88)( 46, 82)( 47, 81)( 48, 85)( 49, 84)( 50, 83)( 51,127)( 52,126)( 53,130)( 54,129)( 55,128)( 56,147)( 57,146)( 58,150)( 59,149)( 60,148)( 61,142)( 62,141)( 63,145)( 64,144)( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,132)( 72,131)( 73,135)( 74,134)( 75,133); poly := sub<Sym(150)|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, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.