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