From: Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry
2D | 3D | |
---|---|---|
Symmetry under rotation only: | ||
Symmetric | 2k - 2 | 3k + c - 3 |
Asymmetric | 2k(o - 1) + 2c - 2 | 3k(o - 1) + 2c - 4 |
Symmetry under rotation and reflection: | ||
Completely symmetric |
2p + b + m - 1 = k - 1 | 3p + 2b + 2m + c - 2 |
Reflection symmetry only |
2p(o - 1) + b(o - 1) + m(o - 1) + c - 1 = k(o - 1) + c - 1 |
If o is even: $3p\left(o-1\right)+b\left(\frac{3}{2}o-1\right)+m\left(\frac{3}{2}o-2\right)+c-2$ If o is odd: $3p\left(o-1\right)+3b\frac{o-1}{2}+3m\frac{o-1}{2}+c-2$ |
Rotational symmetry only |
2p + b + m - 1 = k - 1 | 3p + b + m - 1 |
Completely asymmetric |
2p(o - 1) + b(o - 1) + m(o - 1) + c - 1 = k(o - 1) + c - 1 |
If o is even: $3p\left(o-1\right)+b\left(\frac{3}{2}o-2\right)+m\left(\frac{3}{2}o-1\right)+c-2$ If o is odd: $3p\left(o-1\right)+3b\frac{o-1}{2}+3m\frac{o-1}{2}+c-2$ |