Overview
- Group
- SmallGroup(1800,736)
- Rank
- 4
- Schläfli Type
- {30,15,2}
- Vertices, edges, …
- 30, 225, 15, 2
- Order of s0s1s2s3
- 30
- 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
9-fold
15-fold
25-fold
45-fold
75-fold
Covers minimal covers in bold
None in this atlas.
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)( 26,131)( 27,135)( 28,134)( 29,133)( 30,132)( 31,126)( 32,130)( 33,129)( 34,128)( 35,127)( 36,146)( 37,150)( 38,149)( 39,148)( 40,147)( 41,141)( 42,145)( 43,144)( 44,143)( 45,142)( 46,136)( 47,140)( 48,139)( 49,138)( 50,137)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102)( 61,121)( 62,125)( 63,124)( 64,123)( 65,122)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)(151,156)(152,160)(153,159)(154,158)(155,157)(161,171)(162,175)(163,174)(164,173)(165,172)(167,170)(168,169)(176,206)(177,210)(178,209)(179,208)(180,207)(181,201)(182,205)(183,204)(184,203)(185,202)(186,221)(187,225)(188,224)(189,223)(190,222)(191,216)(192,220)(193,219)(194,218)(195,217)(196,211)(197,215)(198,214)(199,213)(200,212);; s3 := (226,227);; 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*s0*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(227)!( 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(227)!( 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(227)!( 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)( 26,131)( 27,135)( 28,134)( 29,133)( 30,132)( 31,126)( 32,130)( 33,129)( 34,128)( 35,127)( 36,146)( 37,150)( 38,149)( 39,148)( 40,147)( 41,141)( 42,145)( 43,144)( 44,143)( 45,142)( 46,136)( 47,140)( 48,139)( 49,138)( 50,137)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102)( 61,121)( 62,125)( 63,124)( 64,123)( 65,122)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)(151,156)(152,160)(153,159)(154,158)(155,157)(161,171)(162,175)(163,174)(164,173)(165,172)(167,170)(168,169)(176,206)(177,210)(178,209)(179,208)(180,207)(181,201)(182,205)(183,204)(184,203)(185,202)(186,221)(187,225)(188,224)(189,223)(190,222)(191,216)(192,220)(193,219)(194,218)(195,217)(196,211)(197,215)(198,214)(199,213)(200,212); s3 := Sym(227)!(226,227); poly := sub<Sym(227)|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*s0*s1*s0*s1*s2*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 >;