You're quite right, GP is being mistakenly over-broad. Mimivirus (APMV) is an encapsidated virus, and the capsid is what forms that shape. Capsids[1] generally contain the DNA or RNA of the virus' genome and often appear quite geometric. Capsids have a T-number, which determines how many faces of triangles or hexagons+pentagons exist. It's a deeply mathematical field of study since these are, essentially, tiny repetitive building blocks.
Some (tobacco mosaic virus being the most famous) are helical, while others (bacteriophages) look completely different[2]. Viruses appearing spherical are generally enveloped, meaning they contain part of the cellular plasma membrane surrounding their capsid (HIV). Ebola is part of the filovirus family[3], which are characterized by, among other things, their long, filamentous shape (hence the name).
Bacteriophages are often icosahedral in the headpiece. In fact, the packing motor portion of the icosahedral bacteriophage was not solved until recently because the symmetry averaged structure washed out the stalk part in crystallography and cryo-EM techniques. (it was machine-vision-assisted cryo-EM class averaging technique that helped elucidate the structure)
Yes, there are some filamental viruses such as TMV and ebola, and the P22 bacteriophage, but most viruses, even membrane-enveloped ones, seem to have icosahedral or pseudo-icosahedral structures.
My original point being: "d20"-ness is the rule, not the exception.
