Overview
- Group
- SmallGroup(1200,203)
- Rank
- 4
- Schläfli Type
- {6,50,2}
- Vertices, edges, …
- 6, 150, 50, 2
- 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 := ( 26, 51)( 27, 52)( 28, 53)( 29, 54)( 30, 55)( 31, 56)( 32, 57)( 33, 58)( 34, 59)( 35, 60)( 36, 61)( 37, 62)( 38, 63)( 39, 64)( 40, 65)( 41, 66)( 42, 67)( 43, 68)( 44, 69)( 45, 70)( 46, 71)( 47, 72)( 48, 73)( 49, 74)( 50, 75)(101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)(108,133)(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)(115,140)(116,141)(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)(123,148)(124,149)(125,150);; s1 := ( 1, 26)( 2, 30)( 3, 29)( 4, 28)( 5, 27)( 6, 50)( 7, 49)( 8, 48)( 9, 47)( 10, 46)( 11, 45)( 12, 44)( 13, 43)( 14, 42)( 15, 41)( 16, 40)( 17, 39)( 18, 38)( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 33)( 24, 32)( 25, 31)( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 76,101)( 77,105)( 78,104)( 79,103)( 80,102)( 81,125)( 82,124)( 83,123)( 84,122)( 85,121)( 86,120)( 87,119)( 88,118)( 89,117)( 90,116)( 91,115)( 92,114)( 93,113)( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(127,130)(128,129)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)(140,141);; s2 := ( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 76)( 7, 80)( 8, 79)( 9, 78)( 10, 77)( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16, 95)( 17, 94)( 18, 93)( 19, 92)( 20, 91)( 21, 90)( 22, 89)( 23, 88)( 24, 87)( 25, 86)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,101)( 32,105)( 33,104)( 34,103)( 35,102)( 36,125)( 37,124)( 38,123)( 39,122)( 40,121)( 41,120)( 42,119)( 43,118)( 44,117)( 45,116)( 46,115)( 47,114)( 48,113)( 49,112)( 50,111)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)( 56,126)( 57,130)( 58,129)( 59,128)( 60,127)( 61,150)( 62,149)( 63,148)( 64,147)( 65,146)( 66,145)( 67,144)( 68,143)( 69,142)( 70,141)( 71,140)( 72,139)( 73,138)( 74,137)( 75,136);; s3 := (151,152);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*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*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)!( 26, 51)( 27, 52)( 28, 53)( 29, 54)( 30, 55)( 31, 56)( 32, 57)( 33, 58)( 34, 59)( 35, 60)( 36, 61)( 37, 62)( 38, 63)( 39, 64)( 40, 65)( 41, 66)( 42, 67)( 43, 68)( 44, 69)( 45, 70)( 46, 71)( 47, 72)( 48, 73)( 49, 74)( 50, 75)(101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)(108,133)(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)(115,140)(116,141)(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)(123,148)(124,149)(125,150); s1 := Sym(152)!( 1, 26)( 2, 30)( 3, 29)( 4, 28)( 5, 27)( 6, 50)( 7, 49)( 8, 48)( 9, 47)( 10, 46)( 11, 45)( 12, 44)( 13, 43)( 14, 42)( 15, 41)( 16, 40)( 17, 39)( 18, 38)( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 33)( 24, 32)( 25, 31)( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 76,101)( 77,105)( 78,104)( 79,103)( 80,102)( 81,125)( 82,124)( 83,123)( 84,122)( 85,121)( 86,120)( 87,119)( 88,118)( 89,117)( 90,116)( 91,115)( 92,114)( 93,113)( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(127,130)(128,129)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)(140,141); s2 := Sym(152)!( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 76)( 7, 80)( 8, 79)( 9, 78)( 10, 77)( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16, 95)( 17, 94)( 18, 93)( 19, 92)( 20, 91)( 21, 90)( 22, 89)( 23, 88)( 24, 87)( 25, 86)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,101)( 32,105)( 33,104)( 34,103)( 35,102)( 36,125)( 37,124)( 38,123)( 39,122)( 40,121)( 41,120)( 42,119)( 43,118)( 44,117)( 45,116)( 46,115)( 47,114)( 48,113)( 49,112)( 50,111)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)( 56,126)( 57,130)( 58,129)( 59,128)( 60,127)( 61,150)( 62,149)( 63,148)( 64,147)( 65,146)( 66,145)( 67,144)( 68,143)( 69,142)( 70,141)( 71,140)( 72,139)( 73,138)( 74,137)( 75,136); s3 := Sym(152)!(151,152); 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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*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*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 >;