Part of the Atlas of Small Regular Polytopes

Polytope of Type {35,14}

Atlas Canonical Name {35,14}*980

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(980,27)
Rank
3
Schläfli Type
{35,14}
Vertices, edges, …
35, 245, 14
Order of s0s1s2
70
Order of s0s1s2s1
14
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

7-fold

35-fold

49-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := (  2,  7)(  3,  6)(  4,  5)(  8, 43)(  9, 49)( 10, 48)( 11, 47)( 12, 46)( 13, 45)( 14, 44)( 15, 36)( 16, 42)( 17, 41)( 18, 40)( 19, 39)( 20, 38)( 21, 37)( 22, 29)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 50,197)( 51,203)( 52,202)( 53,201)( 54,200)( 55,199)( 56,198)( 57,239)( 58,245)( 59,244)( 60,243)( 61,242)( 62,241)( 63,240)( 64,232)( 65,238)( 66,237)( 67,236)( 68,235)( 69,234)( 70,233)( 71,225)( 72,231)( 73,230)( 74,229)( 75,228)( 76,227)( 77,226)( 78,218)( 79,224)( 80,223)( 81,222)( 82,221)( 83,220)( 84,219)( 85,211)( 86,217)( 87,216)( 88,215)( 89,214)( 90,213)( 91,212)( 92,204)( 93,210)( 94,209)( 95,208)( 96,207)( 97,206)( 98,205)( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(106,190)(107,196)(108,195)(109,194)(110,193)(111,192)(112,191)(113,183)(114,189)(115,188)(116,187)(117,186)(118,185)(119,184)(120,176)(121,182)(122,181)(123,180)(124,179)(125,178)(126,177)(127,169)(128,175)(129,174)(130,173)(131,172)(132,171)(133,170)(134,162)(135,168)(136,167)(137,166)(138,165)(139,164)(140,163)(141,155)(142,161)(143,160)(144,159)(145,158)(146,157)(147,156);;
s1 := (  1, 58)(  2, 57)(  3, 63)(  4, 62)(  5, 61)(  6, 60)(  7, 59)(  8, 51)(  9, 50)( 10, 56)( 11, 55)( 12, 54)( 13, 53)( 14, 52)( 15, 93)( 16, 92)( 17, 98)( 18, 97)( 19, 96)( 20, 95)( 21, 94)( 22, 86)( 23, 85)( 24, 91)( 25, 90)( 26, 89)( 27, 88)( 28, 87)( 29, 79)( 30, 78)( 31, 84)( 32, 83)( 33, 82)( 34, 81)( 35, 80)( 36, 72)( 37, 71)( 38, 77)( 39, 76)( 40, 75)( 41, 74)( 42, 73)( 43, 65)( 44, 64)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 99,205)(100,204)(101,210)(102,209)(103,208)(104,207)(105,206)(106,198)(107,197)(108,203)(109,202)(110,201)(111,200)(112,199)(113,240)(114,239)(115,245)(116,244)(117,243)(118,242)(119,241)(120,233)(121,232)(122,238)(123,237)(124,236)(125,235)(126,234)(127,226)(128,225)(129,231)(130,230)(131,229)(132,228)(133,227)(134,219)(135,218)(136,224)(137,223)(138,222)(139,221)(140,220)(141,212)(142,211)(143,217)(144,216)(145,215)(146,214)(147,213)(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)(154,157)(162,191)(163,190)(164,196)(165,195)(166,194)(167,193)(168,192)(169,184)(170,183)(171,189)(172,188)(173,187)(174,186)(175,185)(176,177)(178,182)(179,181);;
s2 := (  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 36)( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 57, 92)( 58, 93)( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)( 67, 88)( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)(111,146)(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)(164,185)(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182)(204,239)(205,240)(206,241)(207,242)(208,243)(209,244)(210,245)(211,232)(212,233)(213,234)(214,235)(215,236)(216,237)(217,238)(218,225)(219,226)(220,227)(221,228)(222,229)(223,230)(224,231);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(245)!(  2,  7)(  3,  6)(  4,  5)(  8, 43)(  9, 49)( 10, 48)( 11, 47)( 12, 46)( 13, 45)( 14, 44)( 15, 36)( 16, 42)( 17, 41)( 18, 40)( 19, 39)( 20, 38)( 21, 37)( 22, 29)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 50,197)( 51,203)( 52,202)( 53,201)( 54,200)( 55,199)( 56,198)( 57,239)( 58,245)( 59,244)( 60,243)( 61,242)( 62,241)( 63,240)( 64,232)( 65,238)( 66,237)( 67,236)( 68,235)( 69,234)( 70,233)( 71,225)( 72,231)( 73,230)( 74,229)( 75,228)( 76,227)( 77,226)( 78,218)( 79,224)( 80,223)( 81,222)( 82,221)( 83,220)( 84,219)( 85,211)( 86,217)( 87,216)( 88,215)( 89,214)( 90,213)( 91,212)( 92,204)( 93,210)( 94,209)( 95,208)( 96,207)( 97,206)( 98,205)( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(106,190)(107,196)(108,195)(109,194)(110,193)(111,192)(112,191)(113,183)(114,189)(115,188)(116,187)(117,186)(118,185)(119,184)(120,176)(121,182)(122,181)(123,180)(124,179)(125,178)(126,177)(127,169)(128,175)(129,174)(130,173)(131,172)(132,171)(133,170)(134,162)(135,168)(136,167)(137,166)(138,165)(139,164)(140,163)(141,155)(142,161)(143,160)(144,159)(145,158)(146,157)(147,156);
s1 := Sym(245)!(  1, 58)(  2, 57)(  3, 63)(  4, 62)(  5, 61)(  6, 60)(  7, 59)(  8, 51)(  9, 50)( 10, 56)( 11, 55)( 12, 54)( 13, 53)( 14, 52)( 15, 93)( 16, 92)( 17, 98)( 18, 97)( 19, 96)( 20, 95)( 21, 94)( 22, 86)( 23, 85)( 24, 91)( 25, 90)( 26, 89)( 27, 88)( 28, 87)( 29, 79)( 30, 78)( 31, 84)( 32, 83)( 33, 82)( 34, 81)( 35, 80)( 36, 72)( 37, 71)( 38, 77)( 39, 76)( 40, 75)( 41, 74)( 42, 73)( 43, 65)( 44, 64)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 99,205)(100,204)(101,210)(102,209)(103,208)(104,207)(105,206)(106,198)(107,197)(108,203)(109,202)(110,201)(111,200)(112,199)(113,240)(114,239)(115,245)(116,244)(117,243)(118,242)(119,241)(120,233)(121,232)(122,238)(123,237)(124,236)(125,235)(126,234)(127,226)(128,225)(129,231)(130,230)(131,229)(132,228)(133,227)(134,219)(135,218)(136,224)(137,223)(138,222)(139,221)(140,220)(141,212)(142,211)(143,217)(144,216)(145,215)(146,214)(147,213)(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)(154,157)(162,191)(163,190)(164,196)(165,195)(166,194)(167,193)(168,192)(169,184)(170,183)(171,189)(172,188)(173,187)(174,186)(175,185)(176,177)(178,182)(179,181);
s2 := Sym(245)!(  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 36)( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 57, 92)( 58, 93)( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)( 67, 88)( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)(111,146)(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)(164,185)(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182)(204,239)(205,240)(206,241)(207,242)(208,243)(209,244)(210,245)(211,232)(212,233)(213,234)(214,235)(215,236)(216,237)(217,238)(218,225)(219,226)(220,227)(221,228)(222,229)(223,230)(224,231);
poly := sub<Sym(245)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.

Twisty Puzzle