Symmetry in biology Most radially symmetric animals are symmetrical about an axis extending from the center of the oral surface, which contains the mouth to the center of the opposite, , end. Radial symmetry is especially suitable for sessile animals such as the sea anemone, floating animals such as jellyfish, and slow moving organisms such as starfish. Animals in the phyla Cnidaria and Echinodermata are radially symmetric, although many sea anemones and some corals have bilateral symmetry defined by a single structure, the siphonoglyph. Many flowers are radially symmetric or actinomorphic. Roughly identical flower parts – petals, sepals, and stamens – occur at
Klein four-group representation on four points: In this representation, V is a normal subgroup of the alternating group A (and also the symmetric group S) on four letters. In fact, it is the kernel of a surjective group homomorphism from S to S. Other representations within S are: They are not normal subgroups of S According to Galois theory, the existence of the Klein four-group (and in particular, the permutation representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals, as established by Lodovico Ferrari: the map corresponds to the resolvent cubic,