Polytope of Type {2,2,2,2} with group SmallGroup(32,51)

Overview

Group: SmallGroup(32,51)
Rank: 5
Schläfli Type: {2,2,2,2}
Vertices, edges, …: 2, 2, 2, 2, 2
Order of s₀s₁s₂s₃s₄: 2
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat
Self-Dual

Related Polytopes

Constructions

Facet of

{2,2,2,2,2} ·64
{2,2,2,2,3} ·96
{2,2,2,2,4} ·128
{2,2,2,2,5} ·160
{2,2,2,2,6} ·192
{2,2,2,2,7} ·224
{2,2,2,2,8} ·256
{2,2,2,2,9} ·288
{2,2,2,2,10} ·320
{2,2,2,2,11} ·352
{2,2,2,2,12} ·384
{2,2,2,2,13} ·416
{2,2,2,2,14} ·448
{2,2,2,2,15} ·480
{2,2,2,2,16} ·512
{2,2,2,2,17} ·544
{2,2,2,2,18} ·576
{2,2,2,2,19} ·608
{2,2,2,2,20} ·640
{2,2,2,2,21} ·672
{2,2,2,2,22} ·704
{2,2,2,2,23} ·736
{2,2,2,2,24} ·768
{2,2,2,2,25} ·800
{2,2,2,2,26} ·832
{2,2,2,2,27} ·864
{2,2,2,2,28} ·896
{2,2,2,2,29} ·928
{2,2,2,2,30} ·960
{2,2,2,2,31} ·992
{2,2,2,2,33} ·1056
{2,2,2,2,34} ·1088
{2,2,2,2,35} ·1120
{2,2,2,2,36} ·1152
{2,2,2,2,37} ·1184
{2,2,2,2,38} ·1216
{2,2,2,2,39} ·1248
{2,2,2,2,40} ·1280
{2,2,2,2,41} ·1312
{2,2,2,2,42} ·1344
{2,2,2,2,43} ·1376
{2,2,2,2,44} ·1408
{2,2,2,2,45} ·1440
{2,2,2,2,46} ·1472
{2,2,2,2,47} ·1504
{2,2,2,2,49} ·1568
{2,2,2,2,50} ·1600
{2,2,2,2,51} ·1632
{2,2,2,2,52} ·1664
{2,2,2,2,53} ·1696
{2,2,2,2,54} ·1728
{2,2,2,2,55} ·1760
{2,2,2,2,56} ·1792
{2,2,2,2,57} ·1824
{2,2,2,2,58} ·1856
{2,2,2,2,59} ·1888
{2,2,2,2,60} ·1920
{2,2,2,2,61} ·1952
{2,2,2,2,62} ·1984

Vertex figure of

{2,2,2,2,2} ·64
{3,2,2,2,2} ·96
{4,2,2,2,2} ·128
{5,2,2,2,2} ·160
{6,2,2,2,2} ·192
{7,2,2,2,2} ·224
{8,2,2,2,2} ·256
{9,2,2,2,2} ·288
{10,2,2,2,2} ·320
{11,2,2,2,2} ·352
{12,2,2,2,2} ·384
{13,2,2,2,2} ·416
{14,2,2,2,2} ·448
{15,2,2,2,2} ·480
{16,2,2,2,2} ·512
{17,2,2,2,2} ·544
{18,2,2,2,2} ·576
{19,2,2,2,2} ·608
{20,2,2,2,2} ·640
{21,2,2,2,2} ·672
{22,2,2,2,2} ·704
{23,2,2,2,2} ·736
{24,2,2,2,2} ·768
{25,2,2,2,2} ·800
{26,2,2,2,2} ·832
{27,2,2,2,2} ·864
{28,2,2,2,2} ·896
{29,2,2,2,2} ·928
{30,2,2,2,2} ·960
{31,2,2,2,2} ·992
{33,2,2,2,2} ·1056
{34,2,2,2,2} ·1088
{35,2,2,2,2} ·1120
{36,2,2,2,2} ·1152
{37,2,2,2,2} ·1184
{38,2,2,2,2} ·1216
{39,2,2,2,2} ·1248
{40,2,2,2,2} ·1280
{41,2,2,2,2} ·1312
{42,2,2,2,2} ·1344
{43,2,2,2,2} ·1376
{44,2,2,2,2} ·1408
{45,2,2,2,2} ·1440
{46,2,2,2,2} ·1472
{47,2,2,2,2} ·1504
{49,2,2,2,2} ·1568
{50,2,2,2,2} ·1600
{51,2,2,2,2} ·1632
{52,2,2,2,2} ·1664
{53,2,2,2,2} ·1696
{54,2,2,2,2} ·1728
{55,2,2,2,2} ·1760
{56,2,2,2,2} ·1792
{57,2,2,2,2} ·1824
{58,2,2,2,2} ·1856
{59,2,2,2,2} ·1888
{60,2,2,2,2} ·1920
{61,2,2,2,2} ·1952
{62,2,2,2,2} ·1984

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

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Representations

Permutation Representation (GAP)

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (7,8);;
s4 := ( 9,10);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(10)!(1,2);
s1 := Sym(10)!(3,4);
s2 := Sym(10)!(5,6);
s3 := Sym(10)!(7,8);
s4 := Sym(10)!( 9,10);
poly := sub<Sym(10)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4 >;