octagonal prism and decahedron
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There are many such shapes, not just two. Here are some:A nonagonal pyramidAn octagonal prismA square anti-prism (two square faces, with triangles between them)A decahedronA pentagonal bipyramid (two pentagonal pyramids stuck together at their pentagonal faces).Each one is known as a decahedron (plural decahedra).
No shape does. Euler's Formula (vertices + faces = edges + 2) holds true for all shapes. For the given figures, this means: 4 + 6 = 6 + 2 → 10 = 8 but 10 ≠ 8, so the combinations of 4 vertices, 6 edges and 6 faces given does not represent a shape.
A decahedron. Some decahedron shapes are a nonagon-based pyramid, an octagon based prism, or a pentagon based di-pyramid.
If it also has a pentagonal face then a pentagonal pyramid. Else it does not exist.
No, they are not!