Overview
- Group
- SmallGroup(1800,736)
- Rank
- 4
- Schläfli Type
- {2,30,15}
- Vertices, edges, …
- 2, 30, 225, 15
- 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 := (1,2);; s1 := ( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)( 24, 27)( 25, 26)( 28, 53)( 29, 57)( 30, 56)( 31, 55)( 32, 54)( 33, 58)( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 63)( 39, 67)( 40, 66)( 41, 65)( 42, 64)( 43, 68)( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 73)( 49, 77)( 50, 76)( 51, 75)( 52, 74)( 79, 82)( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101)(103,128)(104,132)(105,131)(106,130)(107,129)(108,133)(109,137)(110,136)(111,135)(112,134)(113,138)(114,142)(115,141)(116,140)(117,139)(118,143)(119,147)(120,146)(121,145)(122,144)(123,148)(124,152)(125,151)(126,150)(127,149)(154,157)(155,156)(159,162)(160,161)(164,167)(165,166)(169,172)(170,171)(174,177)(175,176)(178,203)(179,207)(180,206)(181,205)(182,204)(183,208)(184,212)(185,211)(186,210)(187,209)(188,213)(189,217)(190,216)(191,215)(192,214)(193,218)(194,222)(195,221)(196,220)(197,219)(198,223)(199,227)(200,226)(201,225)(202,224);; s2 := ( 3, 29)( 4, 28)( 5, 32)( 6, 31)( 7, 30)( 8, 49)( 9, 48)( 10, 52)( 11, 51)( 12, 50)( 13, 44)( 14, 43)( 15, 47)( 16, 46)( 17, 45)( 18, 39)( 19, 38)( 20, 42)( 21, 41)( 22, 40)( 23, 34)( 24, 33)( 25, 37)( 26, 36)( 27, 35)( 53, 54)( 55, 57)( 58, 74)( 59, 73)( 60, 77)( 61, 76)( 62, 75)( 63, 69)( 64, 68)( 65, 72)( 66, 71)( 67, 70)( 78,179)( 79,178)( 80,182)( 81,181)( 82,180)( 83,199)( 84,198)( 85,202)( 86,201)( 87,200)( 88,194)( 89,193)( 90,197)( 91,196)( 92,195)( 93,189)( 94,188)( 95,192)( 96,191)( 97,190)( 98,184)( 99,183)(100,187)(101,186)(102,185)(103,154)(104,153)(105,157)(106,156)(107,155)(108,174)(109,173)(110,177)(111,176)(112,175)(113,169)(114,168)(115,172)(116,171)(117,170)(118,164)(119,163)(120,167)(121,166)(122,165)(123,159)(124,158)(125,162)(126,161)(127,160)(128,204)(129,203)(130,207)(131,206)(132,205)(133,224)(134,223)(135,227)(136,226)(137,225)(138,219)(139,218)(140,222)(141,221)(142,220)(143,214)(144,213)(145,217)(146,216)(147,215)(148,209)(149,208)(150,212)(151,211)(152,210);; s3 := ( 3, 83)( 4, 87)( 5, 86)( 6, 85)( 7, 84)( 8, 78)( 9, 82)( 10, 81)( 11, 80)( 12, 79)( 13, 98)( 14,102)( 15,101)( 16,100)( 17, 99)( 18, 93)( 19, 97)( 20, 96)( 21, 95)( 22, 94)( 23, 88)( 24, 92)( 25, 91)( 26, 90)( 27, 89)( 28,133)( 29,137)( 30,136)( 31,135)( 32,134)( 33,128)( 34,132)( 35,131)( 36,130)( 37,129)( 38,148)( 39,152)( 40,151)( 41,150)( 42,149)( 43,143)( 44,147)( 45,146)( 46,145)( 47,144)( 48,138)( 49,142)( 50,141)( 51,140)( 52,139)( 53,108)( 54,112)( 55,111)( 56,110)( 57,109)( 58,103)( 59,107)( 60,106)( 61,105)( 62,104)( 63,123)( 64,127)( 65,126)( 66,125)( 67,124)( 68,118)( 69,122)( 70,121)( 71,120)( 72,119)( 73,113)( 74,117)( 75,116)( 76,115)( 77,114)(153,158)(154,162)(155,161)(156,160)(157,159)(163,173)(164,177)(165,176)(166,175)(167,174)(169,172)(170,171)(178,208)(179,212)(180,211)(181,210)(182,209)(183,203)(184,207)(185,206)(186,205)(187,204)(188,223)(189,227)(190,226)(191,225)(192,224)(193,218)(194,222)(195,221)(196,220)(197,219)(198,213)(199,217)(200,216)(201,215)(202,214);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(227)!(1,2); s1 := Sym(227)!( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)( 24, 27)( 25, 26)( 28, 53)( 29, 57)( 30, 56)( 31, 55)( 32, 54)( 33, 58)( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 63)( 39, 67)( 40, 66)( 41, 65)( 42, 64)( 43, 68)( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 73)( 49, 77)( 50, 76)( 51, 75)( 52, 74)( 79, 82)( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101)(103,128)(104,132)(105,131)(106,130)(107,129)(108,133)(109,137)(110,136)(111,135)(112,134)(113,138)(114,142)(115,141)(116,140)(117,139)(118,143)(119,147)(120,146)(121,145)(122,144)(123,148)(124,152)(125,151)(126,150)(127,149)(154,157)(155,156)(159,162)(160,161)(164,167)(165,166)(169,172)(170,171)(174,177)(175,176)(178,203)(179,207)(180,206)(181,205)(182,204)(183,208)(184,212)(185,211)(186,210)(187,209)(188,213)(189,217)(190,216)(191,215)(192,214)(193,218)(194,222)(195,221)(196,220)(197,219)(198,223)(199,227)(200,226)(201,225)(202,224); s2 := Sym(227)!( 3, 29)( 4, 28)( 5, 32)( 6, 31)( 7, 30)( 8, 49)( 9, 48)( 10, 52)( 11, 51)( 12, 50)( 13, 44)( 14, 43)( 15, 47)( 16, 46)( 17, 45)( 18, 39)( 19, 38)( 20, 42)( 21, 41)( 22, 40)( 23, 34)( 24, 33)( 25, 37)( 26, 36)( 27, 35)( 53, 54)( 55, 57)( 58, 74)( 59, 73)( 60, 77)( 61, 76)( 62, 75)( 63, 69)( 64, 68)( 65, 72)( 66, 71)( 67, 70)( 78,179)( 79,178)( 80,182)( 81,181)( 82,180)( 83,199)( 84,198)( 85,202)( 86,201)( 87,200)( 88,194)( 89,193)( 90,197)( 91,196)( 92,195)( 93,189)( 94,188)( 95,192)( 96,191)( 97,190)( 98,184)( 99,183)(100,187)(101,186)(102,185)(103,154)(104,153)(105,157)(106,156)(107,155)(108,174)(109,173)(110,177)(111,176)(112,175)(113,169)(114,168)(115,172)(116,171)(117,170)(118,164)(119,163)(120,167)(121,166)(122,165)(123,159)(124,158)(125,162)(126,161)(127,160)(128,204)(129,203)(130,207)(131,206)(132,205)(133,224)(134,223)(135,227)(136,226)(137,225)(138,219)(139,218)(140,222)(141,221)(142,220)(143,214)(144,213)(145,217)(146,216)(147,215)(148,209)(149,208)(150,212)(151,211)(152,210); s3 := Sym(227)!( 3, 83)( 4, 87)( 5, 86)( 6, 85)( 7, 84)( 8, 78)( 9, 82)( 10, 81)( 11, 80)( 12, 79)( 13, 98)( 14,102)( 15,101)( 16,100)( 17, 99)( 18, 93)( 19, 97)( 20, 96)( 21, 95)( 22, 94)( 23, 88)( 24, 92)( 25, 91)( 26, 90)( 27, 89)( 28,133)( 29,137)( 30,136)( 31,135)( 32,134)( 33,128)( 34,132)( 35,131)( 36,130)( 37,129)( 38,148)( 39,152)( 40,151)( 41,150)( 42,149)( 43,143)( 44,147)( 45,146)( 46,145)( 47,144)( 48,138)( 49,142)( 50,141)( 51,140)( 52,139)( 53,108)( 54,112)( 55,111)( 56,110)( 57,109)( 58,103)( 59,107)( 60,106)( 61,105)( 62,104)( 63,123)( 64,127)( 65,126)( 66,125)( 67,124)( 68,118)( 69,122)( 70,121)( 71,120)( 72,119)( 73,113)( 74,117)( 75,116)( 76,115)( 77,114)(153,158)(154,162)(155,161)(156,160)(157,159)(163,173)(164,177)(165,176)(166,175)(167,174)(169,172)(170,171)(178,208)(179,212)(180,211)(181,210)(182,209)(183,203)(184,207)(185,206)(186,205)(187,204)(188,223)(189,227)(190,226)(191,225)(192,224)(193,218)(194,222)(195,221)(196,220)(197,219)(198,213)(199,217)(200,216)(201,215)(202,214); 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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;