上一片里，🧮 小算盘机器人给积木量了体积、算了表面积。量着量着，它盯上了积木本身：这些形状叫什么？身上有几个面、几条棱、几个尖？这一片，把每块积木拆开来数个遍。Last leaf, the little calculator robot measured volume and worked out surface area. Then it stared at the blocks themselves: what are these shapes called? How many faces, edges and corners does each one have? This leaf, we take every block apart, face by face.
第 1 步：积木家族三大门派Step 1: Three clans of the block family
先看看货架上都站着谁——按“上下一样”和“有没有尖”，它们分成三派。Meet the shelf first — two questions sort them all: do top and bottom match, and is there a point?
柱体像叠起来的硬币：上下两个面一模一样，稳稳站住——圆柱、长方体、三棱柱都属这一派。锥体长着尖脑袋：把柱体的上面缩成一个点，就变成了锥体——圆锥、三棱锥都是。球体处处圆滑：没有平面，没有棱，也没有尖，滚得动、捏不住。Prisms and cylinders stack like coins: top and bottom faces match exactly, so they stand steady — cylinders, cuboids and triangular prisms all belong here. Cones and pyramids wear a pointed cap: shrink a prism's top down to a single point and you get this clan. The sphere is smooth everywhere: no flat face, no edge, no corner — it rolls and won't be pinched.
你可能会想：这些形状身上到底有哪些零件？You might ask: what parts is a solid actually made of?
第 2 步：面、棱、顶点，数一数Step 2: Faces, edges, vertices — count them
平平的面叫“面”；两个面相交的线段叫“棱”；几条棱碰头的尖角叫“顶点”。拿长方体当样本：6 个面、12 条棱、8 个顶点。机器人还发现一个魔法：顶点 − 棱 + 面 = 8 − 12 + 6 = 2，换成任何“没有洞”的立体都成立——这叫欧拉公式（Euler's formula）。A flat side is a face; the line where two faces meet is an edge; the sharp corner where edges meet is a vertex. A cuboid has 6 faces, 12 edges and 8 vertices. The robot even found a magic spell: V − E + F = 8 − 12 + 6 = 2 — and it works for every solid with no holes. It is called Euler's formula.
数完了零件，快递站裁纸板的问题来了：平平的纸板，怎么变成有棱有角的盒子？Parts counted — now the parcel shop needs a box: how does a flat sheet become a box with edges?
第 3 步：把盒子拆开：展开图Step 3: Open the box: nets
沿棱把纸盒剪开、摊平，就得到展开图（net）：6 个正方形排成十字形，虚线是折痕，折起来又变回盒子。同一个立体，剪法不同，展开图也不同——单是正方体，就有 11 种展开图。Cut a box along its edges and flatten it, and you get a net: six squares laid out in a cross, dashed lines marking the folds — fold it back up and the box returns. Slice differently and the net changes: a cube alone has 11 possible nets.
🎮 你来当鉴定师（30 秒）🎮 Your turn: the shape examiner (30 seconds)
道理讲完了。把 4 块积木放上鉴定台：数面、数棱、数顶点、认名字——每答对一题，就多一枚徽章。Theory done. Four blocks go on the judging table: count faces, count edges, count vertices and name the shape — one badge per correct answer.
一句话记住它：立体图形的零件只有三种——平平的面、面与面相交的棱、棱碰头的顶点；柱体上下一样，锥体有尖，球体处处圆滑；沿棱剪开摊平，就是展开图。彩蛋：欧拉公式 V − E + F = 2 对所有“没洞”的立体成立。Remember it in one line: every solid is built from just three parts — flat faces, edges where faces meet, and vertices where edges meet. Prisms match top to bottom, cones and pyramids wear a point, spheres are smooth everywhere; cut along the edges and flatten for a net. Bonus: Euler's formula V − E + F = 2 holds for every solid without holes.
面、棱、顶点：长方体样本 = 6 个面、12 条棱、8 个顶点Faces, edges, vertices: a cuboid has 6 faces, 12 edges, 8 vertices分类看两点：上下两个面是否一样、有没有一个尖Classify by two clues: do the top and bottom match, and is there a point?沿棱剪开摊平 = 展开图；欧拉彩蛋 V − E + F = 2Cut along edges and flatten = a net; the Euler bonus V − E + F = 2
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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