Overview
- Group
- SmallGroup(1800,678)
- Rank
- 3
- Schläfli Type
- {30,30}
- Vertices, edges, …
- 30, 450, 30
- Order of s0s1s2
- 30
- 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
6-fold
9-fold
15-fold
18-fold
25-fold
30-fold
45-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)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)( 22, 25)( 23, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)( 31, 56)( 32, 60)( 33, 59)( 34, 58)( 35, 57)( 36, 61)( 37, 65)( 38, 64)( 39, 63)( 40, 62)( 41, 66)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 71)( 47, 75)( 48, 74)( 49, 73)( 50, 72)( 77, 80)( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)(101,126)(102,130)(103,129)(104,128)(105,127)(106,131)(107,135)(108,134)(109,133)(110,132)(111,136)(112,140)(113,139)(114,138)(115,137)(116,141)(117,145)(118,144)(119,143)(120,142)(121,146)(122,150)(123,149)(124,148)(125,147)(152,155)(153,154)(157,160)(158,159)(162,165)(163,164)(167,170)(168,169)(172,175)(173,174)(176,201)(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)(184,208)(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)(192,220)(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)(200,222);; s1 := ( 1, 27)( 2, 26)( 3, 30)( 4, 29)( 5, 28)( 6, 47)( 7, 46)( 8, 50)( 9, 49)( 10, 48)( 11, 42)( 12, 41)( 13, 45)( 14, 44)( 15, 43)( 16, 37)( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)( 24, 34)( 25, 33)( 51, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76,177)( 77,176)( 78,180)( 79,179)( 80,178)( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)( 86,192)( 87,191)( 88,195)( 89,194)( 90,193)( 91,187)( 92,186)( 93,190)( 94,189)( 95,188)( 96,182)( 97,181)( 98,185)( 99,184)(100,183)(101,152)(102,151)(103,155)(104,154)(105,153)(106,172)(107,171)(108,175)(109,174)(110,173)(111,167)(112,166)(113,170)(114,169)(115,168)(116,162)(117,161)(118,165)(119,164)(120,163)(121,157)(122,156)(123,160)(124,159)(125,158)(126,202)(127,201)(128,205)(129,204)(130,203)(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);; s2 := ( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 76)( 7, 80)( 8, 79)( 9, 78)( 10, 77)( 11, 96)( 12,100)( 13, 99)( 14, 98)( 15, 97)( 16, 91)( 17, 95)( 18, 94)( 19, 93)( 20, 92)( 21, 86)( 22, 90)( 23, 89)( 24, 88)( 25, 87)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,101)( 32,105)( 33,104)( 34,103)( 35,102)( 36,121)( 37,125)( 38,124)( 39,123)( 40,122)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,111)( 47,115)( 48,114)( 49,113)( 50,112)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)( 56,126)( 57,130)( 58,129)( 59,128)( 60,127)( 61,146)( 62,150)( 63,149)( 64,148)( 65,147)( 66,141)( 67,145)( 68,144)( 69,143)( 70,142)( 71,136)( 72,140)( 73,139)( 74,138)( 75,137)(151,156)(152,160)(153,159)(154,158)(155,157)(161,171)(162,175)(163,174)(164,173)(165,172)(167,170)(168,169)(176,181)(177,185)(178,184)(179,183)(180,182)(186,196)(187,200)(188,199)(189,198)(190,197)(192,195)(193,194)(201,206)(202,210)(203,209)(204,208)(205,207)(211,221)(212,225)(213,224)(214,223)(215,222)(217,220)(218,219);; 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*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(225)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)( 22, 25)( 23, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)( 31, 56)( 32, 60)( 33, 59)( 34, 58)( 35, 57)( 36, 61)( 37, 65)( 38, 64)( 39, 63)( 40, 62)( 41, 66)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 71)( 47, 75)( 48, 74)( 49, 73)( 50, 72)( 77, 80)( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)(101,126)(102,130)(103,129)(104,128)(105,127)(106,131)(107,135)(108,134)(109,133)(110,132)(111,136)(112,140)(113,139)(114,138)(115,137)(116,141)(117,145)(118,144)(119,143)(120,142)(121,146)(122,150)(123,149)(124,148)(125,147)(152,155)(153,154)(157,160)(158,159)(162,165)(163,164)(167,170)(168,169)(172,175)(173,174)(176,201)(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)(184,208)(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)(192,220)(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)(200,222); s1 := Sym(225)!( 1, 27)( 2, 26)( 3, 30)( 4, 29)( 5, 28)( 6, 47)( 7, 46)( 8, 50)( 9, 49)( 10, 48)( 11, 42)( 12, 41)( 13, 45)( 14, 44)( 15, 43)( 16, 37)( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)( 24, 34)( 25, 33)( 51, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76,177)( 77,176)( 78,180)( 79,179)( 80,178)( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)( 86,192)( 87,191)( 88,195)( 89,194)( 90,193)( 91,187)( 92,186)( 93,190)( 94,189)( 95,188)( 96,182)( 97,181)( 98,185)( 99,184)(100,183)(101,152)(102,151)(103,155)(104,154)(105,153)(106,172)(107,171)(108,175)(109,174)(110,173)(111,167)(112,166)(113,170)(114,169)(115,168)(116,162)(117,161)(118,165)(119,164)(120,163)(121,157)(122,156)(123,160)(124,159)(125,158)(126,202)(127,201)(128,205)(129,204)(130,203)(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); s2 := Sym(225)!( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 76)( 7, 80)( 8, 79)( 9, 78)( 10, 77)( 11, 96)( 12,100)( 13, 99)( 14, 98)( 15, 97)( 16, 91)( 17, 95)( 18, 94)( 19, 93)( 20, 92)( 21, 86)( 22, 90)( 23, 89)( 24, 88)( 25, 87)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,101)( 32,105)( 33,104)( 34,103)( 35,102)( 36,121)( 37,125)( 38,124)( 39,123)( 40,122)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,111)( 47,115)( 48,114)( 49,113)( 50,112)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)( 56,126)( 57,130)( 58,129)( 59,128)( 60,127)( 61,146)( 62,150)( 63,149)( 64,148)( 65,147)( 66,141)( 67,145)( 68,144)( 69,143)( 70,142)( 71,136)( 72,140)( 73,139)( 74,138)( 75,137)(151,156)(152,160)(153,159)(154,158)(155,157)(161,171)(162,175)(163,174)(164,173)(165,172)(167,170)(168,169)(176,181)(177,185)(178,184)(179,183)(180,182)(186,196)(187,200)(188,199)(189,198)(190,197)(192,195)(193,194)(201,206)(202,210)(203,209)(204,208)(205,207)(211,221)(212,225)(213,224)(214,223)(215,222)(217,220)(218,219); 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*s2*s1*s0*s1*s2*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 >;
References
None.
to this polytope.