Overview
- Group
- SmallGroup(1800,229)
- Rank
- 3
- Schläfli Type
- {150,6}
- Vertices, edges, …
- 150, 450, 6
- Order of s0s1s2
- 150
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
- Self-Petrie
Quotients maximal quotients in bold
3-fold
5-fold
9-fold
15-fold
18-fold
25-fold
45-fold
50-fold
75-fold
90-fold
150-fold
225-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 5)( 3, 4)( 6, 22)( 7, 21)( 8, 25)( 9, 24)( 10, 23)( 11, 17)( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 27, 30)( 28, 29)( 31, 47)( 32, 46)( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)( 52, 55)( 53, 54)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76,151)( 77,155)( 78,154)( 79,153)( 80,152)( 81,172)( 82,171)( 83,175)( 84,174)( 85,173)( 86,167)( 87,166)( 88,170)( 89,169)( 90,168)( 91,162)( 92,161)( 93,165)( 94,164)( 95,163)( 96,157)( 97,156)( 98,160)( 99,159)(100,158)(101,176)(102,180)(103,179)(104,178)(105,177)(106,197)(107,196)(108,200)(109,199)(110,198)(111,192)(112,191)(113,195)(114,194)(115,193)(116,187)(117,186)(118,190)(119,189)(120,188)(121,182)(122,181)(123,185)(124,184)(125,183)(126,201)(127,205)(128,204)(129,203)(130,202)(131,222)(132,221)(133,225)(134,224)(135,223)(136,217)(137,216)(138,220)(139,219)(140,218)(141,212)(142,211)(143,215)(144,214)(145,213)(146,207)(147,206)(148,210)(149,209)(150,208);; s1 := ( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 76)( 7, 80)( 8, 79)( 9, 78)( 10, 77)( 11, 97)( 12, 96)( 13,100)( 14, 99)( 15, 98)( 16, 92)( 17, 91)( 18, 95)( 19, 94)( 20, 93)( 21, 87)( 22, 86)( 23, 90)( 24, 89)( 25, 88)( 26,131)( 27,135)( 28,134)( 29,133)( 30,132)( 31,126)( 32,130)( 33,129)( 34,128)( 35,127)( 36,147)( 37,146)( 38,150)( 39,149)( 40,148)( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,137)( 47,136)( 48,140)( 49,139)( 50,138)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102)( 61,122)( 62,121)( 63,125)( 64,124)( 65,123)( 66,117)( 67,116)( 68,120)( 69,119)( 70,118)( 71,112)( 72,111)( 73,115)( 74,114)( 75,113)(151,156)(152,160)(153,159)(154,158)(155,157)(161,172)(162,171)(163,175)(164,174)(165,173)(166,167)(168,170)(176,206)(177,210)(178,209)(179,208)(180,207)(181,201)(182,205)(183,204)(184,203)(185,202)(186,222)(187,221)(188,225)(189,224)(190,223)(191,217)(192,216)(193,220)(194,219)(195,218)(196,212)(197,211)(198,215)(199,214)(200,213);; s2 := ( 1, 26)( 2, 27)( 3, 28)( 4, 29)( 5, 30)( 6, 31)( 7, 32)( 8, 33)( 9, 34)( 10, 35)( 11, 36)( 12, 37)( 13, 38)( 14, 39)( 15, 40)( 16, 41)( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 46)( 22, 47)( 23, 48)( 24, 49)( 25, 50)( 76,176)( 77,177)( 78,178)( 79,179)( 80,180)( 81,181)( 82,182)( 83,183)( 84,184)( 85,185)( 86,186)( 87,187)( 88,188)( 89,189)( 90,190)( 91,191)( 92,192)( 93,193)( 94,194)( 95,195)( 96,196)( 97,197)( 98,198)( 99,199)(100,200)(101,151)(102,152)(103,153)(104,154)(105,155)(106,156)(107,157)(108,158)(109,159)(110,160)(111,161)(112,162)(113,163)(114,164)(115,165)(116,166)(117,167)(118,168)(119,169)(120,170)(121,171)(122,172)(123,173)(124,174)(125,175)(126,201)(127,202)(128,203)(129,204)(130,205)(131,206)(132,207)(133,208)(134,209)(135,210)(136,211)(137,212)(138,213)(139,214)(140,215)(141,216)(142,217)(143,218)(144,219)(145,220)(146,221)(147,222)(148,223)(149,224)(150,225);; 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*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(225)!( 2, 5)( 3, 4)( 6, 22)( 7, 21)( 8, 25)( 9, 24)( 10, 23)( 11, 17)( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 27, 30)( 28, 29)( 31, 47)( 32, 46)( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)( 52, 55)( 53, 54)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76,151)( 77,155)( 78,154)( 79,153)( 80,152)( 81,172)( 82,171)( 83,175)( 84,174)( 85,173)( 86,167)( 87,166)( 88,170)( 89,169)( 90,168)( 91,162)( 92,161)( 93,165)( 94,164)( 95,163)( 96,157)( 97,156)( 98,160)( 99,159)(100,158)(101,176)(102,180)(103,179)(104,178)(105,177)(106,197)(107,196)(108,200)(109,199)(110,198)(111,192)(112,191)(113,195)(114,194)(115,193)(116,187)(117,186)(118,190)(119,189)(120,188)(121,182)(122,181)(123,185)(124,184)(125,183)(126,201)(127,205)(128,204)(129,203)(130,202)(131,222)(132,221)(133,225)(134,224)(135,223)(136,217)(137,216)(138,220)(139,219)(140,218)(141,212)(142,211)(143,215)(144,214)(145,213)(146,207)(147,206)(148,210)(149,209)(150,208); s1 := Sym(225)!( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 76)( 7, 80)( 8, 79)( 9, 78)( 10, 77)( 11, 97)( 12, 96)( 13,100)( 14, 99)( 15, 98)( 16, 92)( 17, 91)( 18, 95)( 19, 94)( 20, 93)( 21, 87)( 22, 86)( 23, 90)( 24, 89)( 25, 88)( 26,131)( 27,135)( 28,134)( 29,133)( 30,132)( 31,126)( 32,130)( 33,129)( 34,128)( 35,127)( 36,147)( 37,146)( 38,150)( 39,149)( 40,148)( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,137)( 47,136)( 48,140)( 49,139)( 50,138)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102)( 61,122)( 62,121)( 63,125)( 64,124)( 65,123)( 66,117)( 67,116)( 68,120)( 69,119)( 70,118)( 71,112)( 72,111)( 73,115)( 74,114)( 75,113)(151,156)(152,160)(153,159)(154,158)(155,157)(161,172)(162,171)(163,175)(164,174)(165,173)(166,167)(168,170)(176,206)(177,210)(178,209)(179,208)(180,207)(181,201)(182,205)(183,204)(184,203)(185,202)(186,222)(187,221)(188,225)(189,224)(190,223)(191,217)(192,216)(193,220)(194,219)(195,218)(196,212)(197,211)(198,215)(199,214)(200,213); s2 := Sym(225)!( 1, 26)( 2, 27)( 3, 28)( 4, 29)( 5, 30)( 6, 31)( 7, 32)( 8, 33)( 9, 34)( 10, 35)( 11, 36)( 12, 37)( 13, 38)( 14, 39)( 15, 40)( 16, 41)( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 46)( 22, 47)( 23, 48)( 24, 49)( 25, 50)( 76,176)( 77,177)( 78,178)( 79,179)( 80,180)( 81,181)( 82,182)( 83,183)( 84,184)( 85,185)( 86,186)( 87,187)( 88,188)( 89,189)( 90,190)( 91,191)( 92,192)( 93,193)( 94,194)( 95,195)( 96,196)( 97,197)( 98,198)( 99,199)(100,200)(101,151)(102,152)(103,153)(104,154)(105,155)(106,156)(107,157)(108,158)(109,159)(110,160)(111,161)(112,162)(113,163)(114,164)(115,165)(116,166)(117,167)(118,168)(119,169)(120,170)(121,171)(122,172)(123,173)(124,174)(125,175)(126,201)(127,202)(128,203)(129,204)(130,205)(131,206)(132,207)(133,208)(134,209)(135,210)(136,211)(137,212)(138,213)(139,214)(140,215)(141,216)(142,217)(143,218)(144,219)(145,220)(146,221)(147,222)(148,223)(149,224)(150,225); poly := sub<Sym(225)|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*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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.