The Tetrahedron (Res. 256, EVs normalized by 4/3 * PI^2)

Eigenvalues: Data Graph
2D: 1-20 21-40 41-60 61-80 81-100 101-120 121-140 141-160 161-180 181-200    Show No.: Go
3D:    Show No.: Go
Nodal Lines:    Show No.: Go
Nonsingular (identical triangles): 10 (EV=4) 22 (EV=12) 31 (EV=16) 55 (EV=28) 62 (EV=36) 63 (EV=36) 64 (EV=36) 83 (EV=48) 84 (EV=48) 85 (EV=48) 119 (EV=64) 120 (EV=64) 121 (EV=64) 182 (EV=100) 183 (EV=100) 184 (EV=100) 191 (EV=108) 192 (EV=108) 193 (EV=108)
Nonsingular (two types): 19 (EV=9) 46 (EV=25) 49 (EV=27) 88 (EV=49) 136 (EV=75) 151 (EV=81)
Not sure: 44 (EV=25) 45 (EV=25) 47 (EV=27) 48 (EV=27) 134 (EV=75) 135 (EV=75) 149 (EV=81) 150 (EV=81)
Graphs: Counting Function Remainder

The Cube (Res. 128, EVs normalized by PI^2)

Eigenvalues: Data Graph
2D: 1-20 21-40 41-60 61-80 81-100 101-120 121-140 141-160 161-180 181-200    Show No.: Go
3D:    Show No.: Go
Nodal Lines:    Show No.: Go
Nonsingular (identical squares): 37 (EV=8) 76 (EV=16) 94 (EV=20) 95 (EV=20) 153 (EV=32) 171 (EV=36) 190 (EV=40) 191 (EV=40)
Nonsingular (rotated squares): 10 (EV=2) 49 (EV=10) 50 (EV=10) 85 (EV=18) 124 (EV=26) 125 (EV=26) 158 (EV=34) 161 (EV=34)
Slice at y=0 and y=1:    Show No.: Go
Graphs: Counting Function Remainder

The Octahedron (Res. 128, EVs normalized by 4/3 * PI^2)

Eigenvalues: Data Graph
2D: 1-20 21-40 41-60 61-80 81-100 101-120 121-140 141-160 161-180 181-200    Show No.: Go
3D:    Show No.: Go
Nodal Lines:    Show No.: Go
Nonsingular (identical triangles): 19 (EV=5.333) 121 (EV=33.333) 171 (EV=48)
Nonsingular (two types): 5 (EV=1.333) 16 (EV=4) 17 (EV=4) 18 (EV=5.333) 35 (EV=9.333) 42 (EV=12) 43 (EV=12) 56 (EV=16) 57 (EV=16) 77 (EV=21.333) 78 (EV=21.333) 104 (EV=28) 105 (EV=28) 106 (EV=28) 107 (EV=28) 120 (EV=33.333) 131 (EV=36) 132 (EV=36) 172 (EV=48)
Not sure: 182 (EV=49.455) 192 (EV=52.136) 193 (EV=52.136) 194 (EV=52.136) 195 (EV=52.136)
Graphs: Counting Function Remainder

The Icosahedron (Res. 128, EVs normalized by 4/3 * PI^2)

Eigenvalues: Data Graph
2D: 1-20 21-40 41-60 61-80 81-100 101-120 121-140 141-160 161-180 181-200    Show No.: Go
3D:    Show No.: Go
Nodal Lines:    Show No.: Go
Nonsingular (identical triangles): 37 (EV=4) 110 (EV=12) 145 (EV=16)
Graphs: Counting Function Remainder

Contact Information

Robert Strichartz, Cornell University, Department of Mathematics, str@math.cornell.edu
Samuel Wiese, University of Leipzig, Department of Mathematics, sw31hiqa@studserv.uni-leipzig.de