There is a class of compounds $A_nE_m$ formed by element $A$ and element $E$ that adopt cage-like structures. Among them, the general formula for closed-cage structures can be represented as $A_nE_n^{2-}$, while the general formula for open-cage structures can be represented as $A_nE_{n+4}$. It is known that closed-cage structures $A_nE_n^{2-}$ can be transformed into corresponding open-cage structures $A_{n-1}E_{n+3}$ through a certain pattern.

For example, the structure of $A_6E_6^{2-}$ is shown below:

<MultiModal>![[E][*]123[*]4([*]356[E])([E])[*]17([E])[*]45([E])[*]726[E]](/media/uploads/3eb791d8-1ec9-4cb7-9466-1bf051866133.png)</MultiModal>

The structure of $A_5E_9$ is shown below:

<MultiModal>![[E][*]123[*]45([E])([E]6)[*]1([E])([E]5)([E]7)[*]7([E])([E]8)2[*]4368[E]](/media/uploads/e6e54ac2-0d39-4efb-9012-a385c3206e5b.png)</MultiModal>

It is known that the structure of $A_7E_7^{2-}$ is shown below:

<MultiModal>![[E][*]123[*]456([E])[*]78([E])[*]49([E])[*]51([E])[*]297([E])[*]638[E]](/media/uploads/217b63a2-c47a-4aca-87ab-cb25b41b4c9c.png)</MultiModal>

Then, in the structure of $A_6E_{10}$, how many triangular faces are there in the skeleton formed by $A_6$?
有一类由元素$A$和元素$E$形成的化合物$A_nE_m$是笼状结构。其中，闭式笼状结构的通式可用 $A_nE_n^{2-}$表示，开式笼状结构的通式可用 $A_nE_{n+4}$ 表示。已知由闭式笼状结构$A_nE_n^{2-}$能通过某种规律转化为相应的开式笼状结构$A_{n-1}E_{n+3}$。

例如，$A_6E_6^{2-}$的结构如下图

<MultiModal>![[E][*]123[*]4([*]356[E])([E])[*]17([E])[*]45([E])[*]726[E]](/media/uploads/3eb791d8-1ec9-4cb7-9466-1bf051866133.png)</MultiModal>

$A_5E_9$的结构如下图

<MultiModal>![[E][*]123[*]45([E])([E]6)[*]1([E])([E]5)([E]7)[*]7([E])([E]8)2[*]4368[E]](/media/uploads/e6e54ac2-0d39-4efb-9012-a385c3206e5b.png)</MultiModal>

已知$A_7E_7^{2-}$的结构如下图

<MultiModal>![[E][*]123[*]456([E])[*]78([E])[*]49([E])[*]51([E])[*]297([E])[*]638[E]](/media/uploads/217b63a2-c47a-4aca-87ab-cb25b41b4c9c.png)</MultiModal>

那么，$A_6E_{10}$的结构中，$A_6$组成的骨架中有几个三角形面？
4
5
6
7
8
None of the above options are correct
4
5
6
7
8
以上选项均不对
The question examines the structure of borane, with specific information concealed to prevent cheating. Here, $A$ and $E$ represent boron and hydrogen, respectively. Based on observations, $A_5E_9$ is derived from $A_6E_6^{2-}$ by removing one vertex and adding four bridging $E$ atoms. Applying a similar approach to $A_7E_7^{2-}$, the removable vertex can be either from the equatorial plane of the pentagonal bipyramid or a vertex outside the equatorial plane. It is found that the vertices outside the equatorial plane have the highest number of adjacent $A$ atoms, and one of them is removed. (Removing the vertex with the highest connectivity ensures the maximum number of broken bonds due to the removal, providing the most candidate positions for adding bridging $E$ atoms. This allows the bridging $E$ atoms to connect different parts more flexibly and fully, reducing strain and maintaining the stability of the open structure.)

<Checkpoint>[Remove a vertex outside the equatorial plane of the pentagonal bipyramid.](1)</Checkpoint>

After removing one such vertex, the vertices outside the pentagon become the $A$ atoms with the highest bonding count. Therefore, the four bridging $E$ atoms should be added to four of the edges of the pentagon.

This results in the structure of $A_6E_{10}$, as shown below:

<MultiModal>![[E][*]1([*]2345[E])([E]6)([E]7)[*]26([E])([E]8)[*]38([E])[*]59([E])[*]147([E]9)[E]](/media/uploads/896d73aa-e87b-4e55-943e-8bd49e109384.png)</MultiModal>

In $A_6E_{10}$, the $A_6$ framework forms a pentagonal pyramid with five triangular faces. Select B.

<Checkpoint>[There are five triangular faces.](1)</Checkpoint>
题目考察硼烷的结构，为防止作弊隐去了具体信息，$A,E$分别是硼和氢。根据观察，$A_5E_9$由$A_6E_6^{2-}$去掉一个顶点，再补上4个桥$E$得到。以类似的方式处理$A_7E_7^{2-}$，可以去掉的顶点有五角双锥赤道面或赤道面以外的顶点，发现赤道面以外的顶点相邻$A$原子数最多，去掉其中一个。（移除连接度最高的顶点确保因移除原子而断裂的键数量最大化，为添加桥$E$提供了最多的候选位置，使得桥$E$能够更灵活、更充分地连接不同部分，减少应变，并保持开式结构的稳定性。）

<Checkpoint>[去掉五角双锥赤道面以外的顶点。](1)</Checkpoint>

去掉其中一个顶点之后，五边形以外的顶点就是成键最多的$A$了，因此4个桥$E$应该加在五边形的其中4个边上。

由此得$A_6E_{10}$的结构如下图

<MultiModal>![[E][*]1([*]2345[E])([E]6)([E]7)[*]26([E])([E]8)[*]38([E])[*]59([E])[*]147([E]9)[E]](/media/uploads/896d73aa-e87b-4e55-943e-8bd49e109384.png)</MultiModal>

$A_6E_{10}$中$A_6$骨架为五角锥，有5个三角形面，选B。

<Checkpoint>[有5个三角形面。](1)</Checkpoint>