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**Title:**
11种正方体表面展开图及口诀
(11 Types of Cube Nets and Mnemonics)
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**Section: (1-4-1型6种) 口诀: 中间4个一连串, 两边各一随便放**
(1-4-1 Type, 6 variations) Mnemonic: Four in the middle connected in a row, one on each side placed casually.
**Chart Description (Four Cube Nets):**
These are diagrams of cube nets, each consisting of 6 squares connected at their edges. The squares that represent the '1's in the 1-4-1 pattern are highlighted in pink.
* **Net 1.1:** A horizontal row of 4 squares. One square is attached above the leftmost square, and another square is attached below the rightmost square. (Pink highlights: the top-left square and the bottom-right square).
* **Net 1.2:** A horizontal row of 4 squares. One square is attached above the leftmost square, and another square is attached below the second square from the left. (Pink highlights: the top-left square and the square below the second from the left).
* **Net 1.3:** A horizontal row of 4 squares. One square is attached below the second square from the left, and another square is attached below the rightmost square. (Pink highlights: the square below the second from the left, and the bottom-right square).
* **Net 1.4:** A horizontal row of 4 squares. One square is attached below the leftmost square, and another square is attached above the rightmost square. (Pink highlights: the bottom-left square and the top-right square).
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**Section: (2-3-1型3种) 口诀: 二三紧连错一个, 三一相连随便**
(2-3-1 Type, 3 variations) Mnemonic: Two and three are closely connected with one错 (missing/shifted), three and one are connected casually.
**Chart Description (Three Cube Nets):**
These are diagrams of cube nets, each consisting of 6 squares. The squares that represent the '2' and '1' in the 2-3-1 pattern are highlighted in light blue.
* **Net 2.1:** A vertical column of 2 squares. To the right of the bottom square of this column, there is a horizontal row of 3 squares. Below the rightmost square of this 3-row, there is 1 additional square. (Blue highlights: the top two squares forming the '2', and the single square at the bottom-right forming the '1').
* **Net 2.2:** A vertical column of 2 squares. To the right of the bottom square of this column, there is a horizontal row of 3 squares. Below the middle square of this 3-row, there is 1 additional square. (Blue highlights: the top two squares forming the '2', and the single square below the middle of the 3-row forming the '1').
* **Net 2.3:** A vertical column of 2 squares. To the right of the bottom square of this column, there is a horizontal row of 3 squares. Above the rightmost square of this 3-row, there is 1 additional square. (Blue highlights: the top two squares forming the '2', and the single square above the rightmost of the 3-row forming the '1').
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**Section: (2-2-2型1种) 口诀: 两两相连各挪一**
(2-2-2 Type, 1 variation) Mnemonic: Two-by-two connected, each shifted by one.
**Chart Description (One Cube Net):**
This is a diagram of a cube net consisting of 6 squares. Three pairs of squares are connected in a staircase pattern, with each pair shifted one step down and one step to the right relative to the previous pair. The top-left square of each of the three pairs is highlighted in orange.
* **Net 3.1:** A 2x1 vertical block. To its right and one step down, another 2x1 vertical block. To its right and one step down again, a third 2x1 vertical block. (Orange highlights: the top-left square of each of the three 2x1 blocks).
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**Section: (3-3型1种) 口诀: 三个两排一对齐**
(3-3 Type, 1 variation) Mnemonic: Three by two rows, aligned.
**Chart Description (One Cube Net):**
This is a diagram of a cube net consisting of 6 squares arranged in a simple rectangular shape.
* **Net 4.1:** A 2x3 rectangular grid of squares.
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**General Rules/Hints (Dotted Border Box):**
要找两个相对面,切记相隔一个面
(To find two opposite faces, remember to skip one face)
一四一,二三一,一在同侧任意移
(1-4-1, 2-3-1, the '1' can be moved anywhere on the same side)
二二二,阶梯路;两个三,日相连
(2-2-2, staircase path; two 3s, connected like '日' [the character for sun/day, implying a 2x2 block with one side open, or two 3-unit rows forming a 'T' or 'L' shape together])
相邻一层必有日,整体没有凹和田
(Adjacent layers must have a '日' pattern, the overall shape should not have a '凹' [concave] or '田' [field] pattern)
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**Section: 排除法 (Exclusion Method)**
**Chart Description (Three Invalid Cube Net Examples):**
These diagrams show patterns of 6 squares that are *not* valid cube nets, indicated by a red 'X' drawn over them.
* **Invalid Net 5.1:** A horizontal row of 5 squares. One square is attached below the third square from the left. A red 'X' is drawn over the 3rd and 4th squares of the horizontal row.
* **Rule:** “一线不过四” (A single line (of connected squares) cannot exceed four squares in length).
* **Invalid Net 5.2:** A 2x3 grid where the top-right square is missing, creating a concave (凹) shape. A red 'X' is drawn over the bottom two rightmost squares.
* **Invalid Net 5.3:** A 2x2 grid with an additional square attached below its bottom-left square and another additional square attached below its bottom-right square, forming a '田' (field) like pattern. A red 'X' is drawn over the two central squares of the initial 2x2 grid.
* **Rule (for 5.2 and 5.3):** “没有凹和田” (There should be no '凹' (concave) or '田' (field) shapes in the overall net).