Question

A coloured sheet is folded into an octahedron as shown on the left. Which of the options show(s) the \textbf{CORRECT rotated views of the octahedron?}

• A. A
• B. B
• C. C
• D. D

Hint:

For solid-rotation problems: \begin{itemize} \item Focus on adjacency of faces, not their absolute position, \item Rotations preserve orientation; reflections do not, \item Track colours around a common vertex for consistency. \end{itemize}

Answer 1

The Correct Option is A, B, C

Step 1: Observe the coloured net of the octahedron on the left. Each triangular face has a fixed colour adjacency that will remain unchanged after folding and rotation. \bigskip Step 2: When the sheet is folded into an octahedron, opposite faces are not adjacent, and each vertex is formed by four triangular faces meeting together. \bigskip Step 3: Analyze each By checking: \begin{itemize} \item Whether adjacent colours match the original net, \item Whether the orientation can be obtained by a rotation (not reflection), \item Whether the relative positions of colours around a vertex are preserved. \end{itemize} \bigskip Step 4: \begin{itemize} \item A: Matches the correct cyclic order of colours — valid. \item B: Can be obtained by rotating the octahedron — valid. \item C: Also preserves all colour adjacencies — valid. \item Option D: Violates the original colour adjacency — invalid. \end{itemize} \bigskip Final Answer: \[ \boxed{\text{A, B and C}} \] \bigskip