conformity with Eulerãs theorem, F ã₤+ã₤ C =ã₤ E ã₤+ã₤2.
AnothôÙer symôÙmetôÙriôÙcal arôÙrangeôÙment will diôÙvide the surôÙface into fourôÙteen rhombs and eight triôÙanôÙgles. This latôÙter arôÙrangeôÙment is obôÙtained by linkôÙing up the radial rods as follows: aaaa, aba, abcb, bcdc, etc. Here we have again twenty corôÙners, but we have twenty-two faces; the numôÙber of edges, or tanôÙgenôÙtial spicôÙular bars, will be found, thereôÙfore, by the above formula, to be forty. In Haeckelãs figôÙure of PhractôÙasôÙpis proôÙtoôÙtypus we have a spicôÙular skelôÙeôÙton which apôÙpears to be conôÙstructôÙed preôÙcisely upon this plan, and to be deôÙrivôÙable from the faceted polyôÙheôÙdron preôÙcisely after this manner.
In all these latter cases it is the arrangement of the axial rods, or in other words the ãpolar symmetryã of the entire organism, which lies at the root of the