Overview
- Group
- SmallGroup(1200,203)
- Rank
- 4
- Schläfli Type
- {2,50,6}
- Vertices, edges, …
- 2, 50, 150, 6
- Order of s0s1s2s3
- 150
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
6-fold
15-fold
25-fold
30-fold
50-fold
75-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 7)( 5, 6)( 8, 27)( 9, 26)( 10, 25)( 11, 24)( 12, 23)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 29, 32)( 30, 31)( 33, 52)( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 54, 57)( 55, 56)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 79, 82)( 80, 81)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 92, 93)(104,107)(105,106)(108,127)(109,126)(110,125)(111,124)(112,123)(113,122)(114,121)(115,120)(116,119)(117,118)(129,132)(130,131)(133,152)(134,151)(135,150)(136,149)(137,148)(138,147)(139,146)(140,145)(141,144)(142,143);; s2 := ( 3, 8)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 28, 58)( 29, 62)( 30, 61)( 31, 60)( 32, 59)( 33, 53)( 34, 57)( 35, 56)( 36, 55)( 37, 54)( 38, 77)( 39, 76)( 40, 75)( 41, 74)( 42, 73)( 43, 72)( 44, 71)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 65)( 51, 64)( 52, 63)( 78, 83)( 79, 87)( 80, 86)( 81, 85)( 82, 84)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(103,133)(104,137)(105,136)(106,135)(107,134)(108,128)(109,132)(110,131)(111,130)(112,129)(113,152)(114,151)(115,150)(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,143)(123,142)(124,141)(125,140)(126,139)(127,138);; s3 := ( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)( 8,108)( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)( 25,125)( 26,126)( 27,127)( 28, 78)( 29, 79)( 30, 80)( 31, 81)( 32, 82)( 33, 83)( 34, 84)( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)( 40, 90)( 41, 91)( 42, 92)( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)( 48, 98)( 49, 99)( 50,100)( 51,101)( 52,102)( 53,128)( 54,129)( 55,130)( 56,131)( 57,132)( 58,133)( 59,134)( 60,135)( 61,136)( 62,137)( 63,138)( 64,139)( 65,140)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,146)( 72,147)( 73,148)( 74,149)( 75,150)( 76,151)( 77,152);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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*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(152)!(1,2); s1 := Sym(152)!( 4, 7)( 5, 6)( 8, 27)( 9, 26)( 10, 25)( 11, 24)( 12, 23)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 29, 32)( 30, 31)( 33, 52)( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 54, 57)( 55, 56)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 79, 82)( 80, 81)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 92, 93)(104,107)(105,106)(108,127)(109,126)(110,125)(111,124)(112,123)(113,122)(114,121)(115,120)(116,119)(117,118)(129,132)(130,131)(133,152)(134,151)(135,150)(136,149)(137,148)(138,147)(139,146)(140,145)(141,144)(142,143); s2 := Sym(152)!( 3, 8)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 28, 58)( 29, 62)( 30, 61)( 31, 60)( 32, 59)( 33, 53)( 34, 57)( 35, 56)( 36, 55)( 37, 54)( 38, 77)( 39, 76)( 40, 75)( 41, 74)( 42, 73)( 43, 72)( 44, 71)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 65)( 51, 64)( 52, 63)( 78, 83)( 79, 87)( 80, 86)( 81, 85)( 82, 84)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(103,133)(104,137)(105,136)(106,135)(107,134)(108,128)(109,132)(110,131)(111,130)(112,129)(113,152)(114,151)(115,150)(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,143)(123,142)(124,141)(125,140)(126,139)(127,138); s3 := Sym(152)!( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)( 8,108)( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)( 25,125)( 26,126)( 27,127)( 28, 78)( 29, 79)( 30, 80)( 31, 81)( 32, 82)( 33, 83)( 34, 84)( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)( 40, 90)( 41, 91)( 42, 92)( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)( 48, 98)( 49, 99)( 50,100)( 51,101)( 52,102)( 53,128)( 54,129)( 55,130)( 56,131)( 57,132)( 58,133)( 59,134)( 60,135)( 61,136)( 62,137)( 63,138)( 64,139)( 65,140)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,146)( 72,147)( 73,148)( 74,149)( 75,150)( 76,151)( 77,152); poly := sub<Sym(152)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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*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 >;