Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,30}

Atlas Canonical Name {10,30}*1500e

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1500,72)
Rank
3
Schläfli Type
{10,30}
Vertices, edges, …
25, 375, 75
Order of s0s1s2
15
Order of s0s1s2s1
10
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

3-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)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)(161,166)(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)(182,200)(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)(190,192)(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)(240,242)(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)(261,266)(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)(282,300)(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)(290,292)(302,305)(303,304)(306,321)(307,325)(308,324)(309,323)(310,322)(311,316)(312,320)(313,319)(314,318)(315,317)(327,330)(328,329)(331,346)(332,350)(333,349)(334,348)(335,347)(336,341)(337,345)(338,344)(339,343)(340,342)(352,355)(353,354)(356,371)(357,375)(358,374)(359,373)(360,372)(361,366)(362,370)(363,369)(364,368)(365,367);;
s1 := (  1,  6)(  2,  7)(  3,  8)(  4,  9)(  5, 10)( 11, 21)( 12, 22)( 13, 23)( 14, 24)( 15, 25)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,101)( 32,102)( 33,103)( 34,104)( 35,105)( 36,121)( 37,122)( 38,123)( 39,124)( 40,125)( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46,111)( 47,112)( 48,113)( 49,114)( 50,115)( 51, 81)( 52, 82)( 53, 83)( 54, 84)( 55, 85)( 56, 76)( 57, 77)( 58, 78)( 59, 79)( 60, 80)( 61, 96)( 62, 97)( 63, 98)( 64, 99)( 65,100)( 66, 91)( 67, 92)( 68, 93)( 69, 94)( 70, 95)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)(126,256)(127,257)(128,258)(129,259)(130,260)(131,251)(132,252)(133,253)(134,254)(135,255)(136,271)(137,272)(138,273)(139,274)(140,275)(141,266)(142,267)(143,268)(144,269)(145,270)(146,261)(147,262)(148,263)(149,264)(150,265)(151,356)(152,357)(153,358)(154,359)(155,360)(156,351)(157,352)(158,353)(159,354)(160,355)(161,371)(162,372)(163,373)(164,374)(165,375)(166,366)(167,367)(168,368)(169,369)(170,370)(171,361)(172,362)(173,363)(174,364)(175,365)(176,331)(177,332)(178,333)(179,334)(180,335)(181,326)(182,327)(183,328)(184,329)(185,330)(186,346)(187,347)(188,348)(189,349)(190,350)(191,341)(192,342)(193,343)(194,344)(195,345)(196,336)(197,337)(198,338)(199,339)(200,340)(201,306)(202,307)(203,308)(204,309)(205,310)(206,301)(207,302)(208,303)(209,304)(210,305)(211,321)(212,322)(213,323)(214,324)(215,325)(216,316)(217,317)(218,318)(219,319)(220,320)(221,311)(222,312)(223,313)(224,314)(225,315)(226,281)(227,282)(228,283)(229,284)(230,285)(231,276)(232,277)(233,278)(234,279)(235,280)(236,296)(237,297)(238,298)(239,299)(240,300)(241,291)(242,292)(243,293)(244,294)(245,295)(246,286)(247,287)(248,288)(249,289)(250,290);;
s2 := (  1,151)(  2,155)(  3,154)(  4,153)(  5,152)(  6,157)(  7,156)(  8,160)(  9,159)( 10,158)( 11,163)( 12,162)( 13,161)( 14,165)( 15,164)( 16,169)( 17,168)( 18,167)( 19,166)( 20,170)( 21,175)( 22,174)( 23,173)( 24,172)( 25,171)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,132)( 32,131)( 33,135)( 34,134)( 35,133)( 36,138)( 37,137)( 38,136)( 39,140)( 40,139)( 41,144)( 42,143)( 43,142)( 44,141)( 45,145)( 46,150)( 47,149)( 48,148)( 49,147)( 50,146)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)( 56,232)( 57,231)( 58,235)( 59,234)( 60,233)( 61,238)( 62,237)( 63,236)( 64,240)( 65,239)( 66,244)( 67,243)( 68,242)( 69,241)( 70,245)( 71,250)( 72,249)( 73,248)( 74,247)( 75,246)( 76,201)( 77,205)( 78,204)( 79,203)( 80,202)( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,213)( 87,212)( 88,211)( 89,215)( 90,214)( 91,219)( 92,218)( 93,217)( 94,216)( 95,220)( 96,225)( 97,224)( 98,223)( 99,222)(100,221)(101,176)(102,180)(103,179)(104,178)(105,177)(106,182)(107,181)(108,185)(109,184)(110,183)(111,188)(112,187)(113,186)(114,190)(115,189)(116,194)(117,193)(118,192)(119,191)(120,195)(121,200)(122,199)(123,198)(124,197)(125,196)(251,276)(252,280)(253,279)(254,278)(255,277)(256,282)(257,281)(258,285)(259,284)(260,283)(261,288)(262,287)(263,286)(264,290)(265,289)(266,294)(267,293)(268,292)(269,291)(270,295)(271,300)(272,299)(273,298)(274,297)(275,296)(301,351)(302,355)(303,354)(304,353)(305,352)(306,357)(307,356)(308,360)(309,359)(310,358)(311,363)(312,362)(313,361)(314,365)(315,364)(316,369)(317,368)(318,367)(319,366)(320,370)(321,375)(322,374)(323,373)(324,372)(325,371)(327,330)(328,329)(331,332)(333,335)(336,338)(339,340)(341,344)(342,343)(346,350)(347,349);;
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*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
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*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(375)!(  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)(161,166)(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)(182,200)(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)(190,192)(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)(240,242)(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)(261,266)(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)(282,300)(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)(290,292)(302,305)(303,304)(306,321)(307,325)(308,324)(309,323)(310,322)(311,316)(312,320)(313,319)(314,318)(315,317)(327,330)(328,329)(331,346)(332,350)(333,349)(334,348)(335,347)(336,341)(337,345)(338,344)(339,343)(340,342)(352,355)(353,354)(356,371)(357,375)(358,374)(359,373)(360,372)(361,366)(362,370)(363,369)(364,368)(365,367);
s1 := Sym(375)!(  1,  6)(  2,  7)(  3,  8)(  4,  9)(  5, 10)( 11, 21)( 12, 22)( 13, 23)( 14, 24)( 15, 25)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,101)( 32,102)( 33,103)( 34,104)( 35,105)( 36,121)( 37,122)( 38,123)( 39,124)( 40,125)( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46,111)( 47,112)( 48,113)( 49,114)( 50,115)( 51, 81)( 52, 82)( 53, 83)( 54, 84)( 55, 85)( 56, 76)( 57, 77)( 58, 78)( 59, 79)( 60, 80)( 61, 96)( 62, 97)( 63, 98)( 64, 99)( 65,100)( 66, 91)( 67, 92)( 68, 93)( 69, 94)( 70, 95)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)(126,256)(127,257)(128,258)(129,259)(130,260)(131,251)(132,252)(133,253)(134,254)(135,255)(136,271)(137,272)(138,273)(139,274)(140,275)(141,266)(142,267)(143,268)(144,269)(145,270)(146,261)(147,262)(148,263)(149,264)(150,265)(151,356)(152,357)(153,358)(154,359)(155,360)(156,351)(157,352)(158,353)(159,354)(160,355)(161,371)(162,372)(163,373)(164,374)(165,375)(166,366)(167,367)(168,368)(169,369)(170,370)(171,361)(172,362)(173,363)(174,364)(175,365)(176,331)(177,332)(178,333)(179,334)(180,335)(181,326)(182,327)(183,328)(184,329)(185,330)(186,346)(187,347)(188,348)(189,349)(190,350)(191,341)(192,342)(193,343)(194,344)(195,345)(196,336)(197,337)(198,338)(199,339)(200,340)(201,306)(202,307)(203,308)(204,309)(205,310)(206,301)(207,302)(208,303)(209,304)(210,305)(211,321)(212,322)(213,323)(214,324)(215,325)(216,316)(217,317)(218,318)(219,319)(220,320)(221,311)(222,312)(223,313)(224,314)(225,315)(226,281)(227,282)(228,283)(229,284)(230,285)(231,276)(232,277)(233,278)(234,279)(235,280)(236,296)(237,297)(238,298)(239,299)(240,300)(241,291)(242,292)(243,293)(244,294)(245,295)(246,286)(247,287)(248,288)(249,289)(250,290);
s2 := Sym(375)!(  1,151)(  2,155)(  3,154)(  4,153)(  5,152)(  6,157)(  7,156)(  8,160)(  9,159)( 10,158)( 11,163)( 12,162)( 13,161)( 14,165)( 15,164)( 16,169)( 17,168)( 18,167)( 19,166)( 20,170)( 21,175)( 22,174)( 23,173)( 24,172)( 25,171)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,132)( 32,131)( 33,135)( 34,134)( 35,133)( 36,138)( 37,137)( 38,136)( 39,140)( 40,139)( 41,144)( 42,143)( 43,142)( 44,141)( 45,145)( 46,150)( 47,149)( 48,148)( 49,147)( 50,146)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)( 56,232)( 57,231)( 58,235)( 59,234)( 60,233)( 61,238)( 62,237)( 63,236)( 64,240)( 65,239)( 66,244)( 67,243)( 68,242)( 69,241)( 70,245)( 71,250)( 72,249)( 73,248)( 74,247)( 75,246)( 76,201)( 77,205)( 78,204)( 79,203)( 80,202)( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,213)( 87,212)( 88,211)( 89,215)( 90,214)( 91,219)( 92,218)( 93,217)( 94,216)( 95,220)( 96,225)( 97,224)( 98,223)( 99,222)(100,221)(101,176)(102,180)(103,179)(104,178)(105,177)(106,182)(107,181)(108,185)(109,184)(110,183)(111,188)(112,187)(113,186)(114,190)(115,189)(116,194)(117,193)(118,192)(119,191)(120,195)(121,200)(122,199)(123,198)(124,197)(125,196)(251,276)(252,280)(253,279)(254,278)(255,277)(256,282)(257,281)(258,285)(259,284)(260,283)(261,288)(262,287)(263,286)(264,290)(265,289)(266,294)(267,293)(268,292)(269,291)(270,295)(271,300)(272,299)(273,298)(274,297)(275,296)(301,351)(302,355)(303,354)(304,353)(305,352)(306,357)(307,356)(308,360)(309,359)(310,358)(311,363)(312,362)(313,361)(314,365)(315,364)(316,369)(317,368)(318,367)(319,366)(320,370)(321,375)(322,374)(323,373)(324,372)(325,371)(327,330)(328,329)(331,332)(333,335)(336,338)(339,340)(341,344)(342,343)(346,350)(347,349);
poly := sub<Sym(375)|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*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
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*s0*s1*s2*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 >;

References

None.

to this polytope.

Twisty Puzzle