Step 1: Understanding the Concept:
This question tests two independent concepts in virology: viral genome organization and the geometry of viral capsid symmetry.
Most vertebrate viruses possess a haploid genome, while the icosahedron is the common geometric shape of many viral capsids.
Detailed Explanation:
Statement I:
The statement is incorrect because the genome of vertebrate viruses is generally haploid, not diploid.
Only members of the family Retroviridae possess two identical copies of single-stranded RNA and are described as diploid.
Since this is an exception rather than the general rule, Statement I is false.
Statement II:
An icosahedron is a regular polyhedron commonly found in viral capsids.
Its geometric properties are:
- 20 triangular faces,
- 30 edges,
- 12 vertices.
Therefore, Statement II is true.
Step 2: Final Answer:
Statement I is false, whereas Statement II is true.
\[
\boxed{(D) Statement I is false but Statement II is true.
\]