An icosahedral virus is a virus consisting of identical subunits that make up equilateral triangles that are, in turn, arranged in a symmetrical fashion. A special type of icosahedral shape, called a prolate, is a variant of the icosahedral viral shape and is found in bacteriophages.rtem is a doctor of veterinary medicine and has taught science and medicine at the college level. Learn about the different shapes viruses can have, such as helical, icosahedral, prolate, complex and enveloped. Find out why one shape is particularly useful from an energetic standpoint.