Overview
- Group
- SmallGroup(1800,296)
- Rank
- 3
- Schläfli Type
- {10,90}
- Vertices, edges, …
- 10, 450, 90
- Order of s0s1s2
- 90
- 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
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 := ( 4, 13)( 5, 14)( 6, 15)( 7, 10)( 8, 11)( 9, 12)( 16, 61)( 17, 62)( 18, 63)( 19, 73)( 20, 74)( 21, 75)( 22, 70)( 23, 71)( 24, 72)( 25, 67)( 26, 68)( 27, 69)( 28, 64)( 29, 65)( 30, 66)( 31, 46)( 32, 47)( 33, 48)( 34, 58)( 35, 59)( 36, 60)( 37, 55)( 38, 56)( 39, 57)( 40, 52)( 41, 53)( 42, 54)( 43, 49)( 44, 50)( 45, 51)( 79, 88)( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)( 91,136)( 92,137)( 93,138)( 94,148)( 95,149)( 96,150)( 97,145)( 98,146)( 99,147)(100,142)(101,143)(102,144)(103,139)(104,140)(105,141)(106,121)(107,122)(108,123)(109,133)(110,134)(111,135)(112,130)(113,131)(114,132)(115,127)(116,128)(117,129)(118,124)(119,125)(120,126)(154,163)(155,164)(156,165)(157,160)(158,161)(159,162)(166,211)(167,212)(168,213)(169,223)(170,224)(171,225)(172,220)(173,221)(174,222)(175,217)(176,218)(177,219)(178,214)(179,215)(180,216)(181,196)(182,197)(183,198)(184,208)(185,209)(186,210)(187,205)(188,206)(189,207)(190,202)(191,203)(192,204)(193,199)(194,200)(195,201);; s1 := ( 1, 19)( 2, 21)( 3, 20)( 4, 16)( 5, 18)( 6, 17)( 7, 28)( 8, 30)( 9, 29)( 10, 25)( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 31, 64)( 32, 66)( 33, 65)( 34, 61)( 35, 63)( 36, 62)( 37, 73)( 38, 75)( 39, 74)( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 49)( 47, 51)( 48, 50)( 52, 58)( 53, 60)( 54, 59)( 56, 57)( 76,170)( 77,169)( 78,171)( 79,167)( 80,166)( 81,168)( 82,179)( 83,178)( 84,180)( 85,176)( 86,175)( 87,177)( 88,173)( 89,172)( 90,174)( 91,155)( 92,154)( 93,156)( 94,152)( 95,151)( 96,153)( 97,164)( 98,163)( 99,165)(100,161)(101,160)(102,162)(103,158)(104,157)(105,159)(106,215)(107,214)(108,216)(109,212)(110,211)(111,213)(112,224)(113,223)(114,225)(115,221)(116,220)(117,222)(118,218)(119,217)(120,219)(121,200)(122,199)(123,201)(124,197)(125,196)(126,198)(127,209)(128,208)(129,210)(130,206)(131,205)(132,207)(133,203)(134,202)(135,204)(136,185)(137,184)(138,186)(139,182)(140,181)(141,183)(142,194)(143,193)(144,195)(145,191)(146,190)(147,192)(148,188)(149,187)(150,189);; s2 := ( 1, 76)( 2, 78)( 3, 77)( 4, 79)( 5, 81)( 6, 80)( 7, 82)( 8, 84)( 9, 83)( 10, 85)( 11, 87)( 12, 86)( 13, 88)( 14, 90)( 15, 89)( 16,136)( 17,138)( 18,137)( 19,139)( 20,141)( 21,140)( 22,142)( 23,144)( 24,143)( 25,145)( 26,147)( 27,146)( 28,148)( 29,150)( 30,149)( 31,121)( 32,123)( 33,122)( 34,124)( 35,126)( 36,125)( 37,127)( 38,129)( 39,128)( 40,130)( 41,132)( 42,131)( 43,133)( 44,135)( 45,134)( 46,106)( 47,108)( 48,107)( 49,109)( 50,111)( 51,110)( 52,112)( 53,114)( 54,113)( 55,115)( 56,117)( 57,116)( 58,118)( 59,120)( 60,119)( 61, 91)( 62, 93)( 63, 92)( 64, 94)( 65, 96)( 66, 95)( 67, 97)( 68, 99)( 69, 98)( 70,100)( 71,102)( 72,101)( 73,103)( 74,105)( 75,104)(151,152)(154,155)(157,158)(160,161)(163,164)(166,212)(167,211)(168,213)(169,215)(170,214)(171,216)(172,218)(173,217)(174,219)(175,221)(176,220)(177,222)(178,224)(179,223)(180,225)(181,197)(182,196)(183,198)(184,200)(185,199)(186,201)(187,203)(188,202)(189,204)(190,206)(191,205)(192,207)(193,209)(194,208)(195,210);; 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*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,
s2*s0*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*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(225)!( 4, 13)( 5, 14)( 6, 15)( 7, 10)( 8, 11)( 9, 12)( 16, 61)( 17, 62)( 18, 63)( 19, 73)( 20, 74)( 21, 75)( 22, 70)( 23, 71)( 24, 72)( 25, 67)( 26, 68)( 27, 69)( 28, 64)( 29, 65)( 30, 66)( 31, 46)( 32, 47)( 33, 48)( 34, 58)( 35, 59)( 36, 60)( 37, 55)( 38, 56)( 39, 57)( 40, 52)( 41, 53)( 42, 54)( 43, 49)( 44, 50)( 45, 51)( 79, 88)( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)( 91,136)( 92,137)( 93,138)( 94,148)( 95,149)( 96,150)( 97,145)( 98,146)( 99,147)(100,142)(101,143)(102,144)(103,139)(104,140)(105,141)(106,121)(107,122)(108,123)(109,133)(110,134)(111,135)(112,130)(113,131)(114,132)(115,127)(116,128)(117,129)(118,124)(119,125)(120,126)(154,163)(155,164)(156,165)(157,160)(158,161)(159,162)(166,211)(167,212)(168,213)(169,223)(170,224)(171,225)(172,220)(173,221)(174,222)(175,217)(176,218)(177,219)(178,214)(179,215)(180,216)(181,196)(182,197)(183,198)(184,208)(185,209)(186,210)(187,205)(188,206)(189,207)(190,202)(191,203)(192,204)(193,199)(194,200)(195,201); s1 := Sym(225)!( 1, 19)( 2, 21)( 3, 20)( 4, 16)( 5, 18)( 6, 17)( 7, 28)( 8, 30)( 9, 29)( 10, 25)( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 31, 64)( 32, 66)( 33, 65)( 34, 61)( 35, 63)( 36, 62)( 37, 73)( 38, 75)( 39, 74)( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 49)( 47, 51)( 48, 50)( 52, 58)( 53, 60)( 54, 59)( 56, 57)( 76,170)( 77,169)( 78,171)( 79,167)( 80,166)( 81,168)( 82,179)( 83,178)( 84,180)( 85,176)( 86,175)( 87,177)( 88,173)( 89,172)( 90,174)( 91,155)( 92,154)( 93,156)( 94,152)( 95,151)( 96,153)( 97,164)( 98,163)( 99,165)(100,161)(101,160)(102,162)(103,158)(104,157)(105,159)(106,215)(107,214)(108,216)(109,212)(110,211)(111,213)(112,224)(113,223)(114,225)(115,221)(116,220)(117,222)(118,218)(119,217)(120,219)(121,200)(122,199)(123,201)(124,197)(125,196)(126,198)(127,209)(128,208)(129,210)(130,206)(131,205)(132,207)(133,203)(134,202)(135,204)(136,185)(137,184)(138,186)(139,182)(140,181)(141,183)(142,194)(143,193)(144,195)(145,191)(146,190)(147,192)(148,188)(149,187)(150,189); s2 := Sym(225)!( 1, 76)( 2, 78)( 3, 77)( 4, 79)( 5, 81)( 6, 80)( 7, 82)( 8, 84)( 9, 83)( 10, 85)( 11, 87)( 12, 86)( 13, 88)( 14, 90)( 15, 89)( 16,136)( 17,138)( 18,137)( 19,139)( 20,141)( 21,140)( 22,142)( 23,144)( 24,143)( 25,145)( 26,147)( 27,146)( 28,148)( 29,150)( 30,149)( 31,121)( 32,123)( 33,122)( 34,124)( 35,126)( 36,125)( 37,127)( 38,129)( 39,128)( 40,130)( 41,132)( 42,131)( 43,133)( 44,135)( 45,134)( 46,106)( 47,108)( 48,107)( 49,109)( 50,111)( 51,110)( 52,112)( 53,114)( 54,113)( 55,115)( 56,117)( 57,116)( 58,118)( 59,120)( 60,119)( 61, 91)( 62, 93)( 63, 92)( 64, 94)( 65, 96)( 66, 95)( 67, 97)( 68, 99)( 69, 98)( 70,100)( 71,102)( 72,101)( 73,103)( 74,105)( 75,104)(151,152)(154,155)(157,158)(160,161)(163,164)(166,212)(167,211)(168,213)(169,215)(170,214)(171,216)(172,218)(173,217)(174,219)(175,221)(176,220)(177,222)(178,224)(179,223)(180,225)(181,197)(182,196)(183,198)(184,200)(185,199)(186,201)(187,203)(188,202)(189,204)(190,206)(191,205)(192,207)(193,209)(194,208)(195,210); 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, 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, s2*s0*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*s0*s1*s2*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.