net-folding-face-adjacency
Given a 2D net of a polyhedron (typically cube, tetrahedron, or octahedron) with labels or markings on the faces, determine which faces are adjacent (share an edge) or opposite once the net is folded into 3D. The decisive move is tracking which net edges glue together during folding, often by rotating around a single fold axis at a time.
풀이 전략
- Swap cube for octahedron — face count doubles, but the edge-gluing argument is structurally identical
- Move the cut/fold sequence so a different face becomes the 'anchor' that stays still
- Replace 'which face is adjacent to Q?' with 'which face is opposite to Q?' to flip the target relation
세부 유형 분포 (3)
한 줄을 클릭하면 그 안의 문제를 볼 수 있어요.
- fold-net-to-position-face 50% (2)
Student is given a 2D net (cube, octahedron, etc.) with labeled faces and must mentally fold it to determine which face ends up opposite to — or in a specified adjacent position relative to — a target face. Pure positional bookkeeping: fix one face, track hinged neighbors, use strip rules (e.g., outer squares of a straight 3-strip become opposite faces).
- multi-view-adjacency-deduction 25% (1)
No net is provided. The student is given several corner views of an assembled polyhedron and must reconstruct the face-adjacency graph by noting that faces meeting at a visible vertex are pairwise adjacent. Pivoting on a face that appears in every view assembles its full neighbor set, then complement reasoning (six faces minus pivot minus four neighbors) identifies the opposite face.
- net-to-metric-extraction 25% (1)
Student is given a 2D net of a prism or other solid with some labeled lengths and must (mentally) fold it to identify which net segments become which 3D edges — which lateral edges glue together and which are legs of a base polygon. The output is a numerical measurement (height, base area, volume), obtained by combining net-edge equalities with standard formulas.
더 보기 (연도 추세, 도구 fingerprint, 학년 분포, 전체 문제)
도구 fingerprint (1–17)
학년 분포
- K 1
- Gr 6 2
- Gr 7 1