If you wish to communicate information, I suggest you call it a 30-sided polyhedron or a 30-hedron. Although the prefix for 30 is triaconta so that the "proper" name is triacontahedron, I suggest you keep it simple. Not only is the use of long Greek prefices pretentious, you will only annoy the reader who will probably have to consult a dictionary.
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A 30 sided polygon is known as a Triacontagon.
An icosahedron is a 20-sided figure. It also has 30 edges.
I find the name "30-sided polygon", "40-sided polygon", etc. just fine.
A 30 sided shape is called a Triacontagon.
A triacontagon is a thirty-sided polygon.