16. China has a long history of stone and seal culture, and seals are representatives of this culture. Seals are usually shaped as rectangular prisms, cubes, or cylinders, but the seal of the official Dugu Xin from the Northern and Southern Dynasties is shaped as a ``semi-regular polyhedron'' (Figure 1). A semi-regular polyhedron is a polyhedron formed by two or more types of regular polygons. Semi-regular polyhedra embody the symmetry beauty of mathematics. Figure 2 shows a semi-regular polyhedron with 48 edges, with all vertices on the surface of a cube with edge length 1. This semi-regular polyhedron has $\_\_\_\_$ faces, and its edge length is $\_\_\_\_$. (The first blank is worth 2 points, the second blank is worth 3 points.)

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ba68dcdb-ba59-4e4a-a826-ca351fb7dd81-3_277_296_1690_730}
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\caption{Figure 1}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ba68dcdb-ba59-4e4a-a826-ca351fb7dd81-3_275_273_1695_1059}
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\caption{Figure 2}
\end{center}
\end{figure}

III. Solution Questions: 70 points total. Solutions should include written explanations, proofs, or calculation steps. Questions 17--21 are required questions that all candidates must answer. Questions 22 and 23 are optional questions; candidates should answer according to requirements.\\
(I) Required Questions: 60 points total.\\