The following two figures describe the crystal structure of a mineral (the coordinate system is a right-handed system):

Figure A. $c$-axis projection

<MultiModal>![This is a structural diagram showing a square frame outlined by thin black lines. Inside this frame are 4 spheres of each of two colors. Specifically, for the large green spheres, their coordinates are approximately $(\frac{1}{8}, \frac{1}{8})(\frac{3}{8},\frac{7}{8})(\frac{5}{8},\frac{3}{8})(\frac{7}{8},\frac{5}{8})$; for the small silver spheres, their coordinates are approximately $(\frac{5}{6},\frac{5}{6})(\frac{4}{6},\frac{1}{6})(\frac{2}{6},\frac{4}{6})(\frac{1}{6},\frac{2}{6})$. The lower left of the image marks the axes: horizontal to the right is the $a$-axis, vertical upwards is the $b$-axis, and the center is the origin. The lower right of the image is a legend: the green sphere has the text "Fe+0" to its right, and the silver sphere has the text "Si+0" to its right.](/media/uploads/0ee25a4f-db15-4fc8-9e10-683f84e6f800.png)</MultiModal>

Figure B $[111]$ direction projection

<MultiModal>![This is a structural diagram showing a hexagonal frame outlined by thin black lines (the upper and lower opposite sides are horizontal), and 6 thin black lines connect the center of the hexagon to the 6 vertices, dividing the hexagon into 6 equilateral triangles. Inside this frame are 4 spheres of each of two colors. Specifically, there is 1 large green sphere and 1 small silver sphere at the center of the hexagon, the small sphere is not obscured by the large sphere; each of the 6 equilateral triangles has 1 sphere, with the bottom, top left, and top right being large green spheres, and the top, bottom right, and bottom left being small silver spheres. The distance between these 6 spheres and the center is between $\frac{1}{3}$ and $\frac{2}{3}$ of the side length of the hexagon, and none of these 6 spheres are on the angle bisector of the equilateral triangles. The entire image has 3-fold rotational symmetry. The lower left of the image marks the axes: horizontal to the right is the $a$-axis, the $b$-axis is at a $60\degree$ angle to the horizontal line in the top left, the $c$-axis is at a $60\degree$ angle to the horizontal line in the bottom left, and the center is the origin. The lower right of the image is a legend: the green sphere has the text "Fe+0" to its right, and the silver sphere has the text "Si+0" to its right.](/media/uploads/89547432-e552-4bba-92fb-7c6fb3d8160b.png)</MultiModal>

Select the option combination that contains the most correct descriptions

1. Chemical formula is $\rm FeSi$
2. Crystal structure contains a center of symmetry
3. Crystal structure contains a threefold rotoinversion axis
4. Crystal structure contains a $2_1$ screw axis
5. The 4 identical atoms in the unit cell shown form a regular tetrahedron
6. All atoms in the unit cell are located at the position with the highest symmetry in their space group
7. The space group number is greater than 210
8. The space group number is less than or equal to 210
以下两图描述了一种矿石的晶体结构（坐标系为右手系）：

图A. $c$轴投影

<MultiModal>![这是一张结构示意图，显示了一个由黑色细线勾勒出的正方形边框。在这个边框的内部分布着两种颜色的圆球各4个。具体来说，对于绿色大球，其坐标近似于$(\frac{1}{8}, \frac{1}{8})(\frac{3}{8},\frac{7}{8})(\frac{5}{8},\frac{3}{8})(\frac{7}{8},\frac{5}{8})$；对于银色小球，其坐标近似于$(\frac{5}{6},\frac{5}{6})(\frac{4}{6},\frac{1}{6})(\frac{2}{6},\frac{4}{6})(\frac{1}{6},\frac{2}{6})$。图片左下部标记了轴向：水平向右为$a$轴，竖直向上为$b$轴，中心为原点。图片右下部为图例：绿色球右侧为文字“Fe+0”，银色球右侧为文字“Si+0”。](/media/uploads/0ee25a4f-db15-4fc8-9e10-683f84e6f800.png)</MultiModal>

图B $[111]$ 方向投影

<MultiModal>![这是一张结构示意图，显示了一个由黑色细线勾勒出的正六边形边框（上下两个对边水平），此外还有6条黑色细线连接正六边形中心和6个顶点，并将正六边形分割为6个正三角形。在这个边框内部分布着两种颜色的圆球各4个。具体来说，正六边形中心有1个绿色大球和1个银色小球，小球未被大球遮挡；在6个正三角形中各有1个球，其中正下方、左上方、右上方为绿色大球，正上方、右下方、左下方为银色小球，这6个球与中心的距离在正六边形边长的$\frac{1}{3}$至$\frac{2}{3}$之间，且这6个球均不在正三角形的角平分线上。整张图具有3重旋转对称性。图片左下部标记了轴向：水平向右的是$a$轴，左上与水平线成$60\degree$角的是$b$轴，左下与水平线成$60\degree$角的是$c$轴，中心为原点。图片右下部为图例：绿色球右侧为文字“Fe+0”，银色球右侧为文字“Si+0”。](/media/uploads/89547432-e552-4bba-92fb-7c6fb3d8160b.png)</MultiModal>

选出包含正确描述最多的选项组合

1. 化学式为$\rm FeSi$
2. 晶体结构中含有对称中心
3. 晶体结构中含有三重反轴
4. 晶体结构中含有$2_1$螺旋轴
5. 图示晶胞中4个相同原子组成正四面体
6. 晶胞中所有原子均处在所属空间群中对称性最高的位置
7. 所属空间群编号大于210
8. 所属空间群编号小于或等于210
1 2 5
3 4 5
1 3 4 6
1 3 5 8
1 2 4 6 7
4 5 6 8
1 4 6 8
There is more than one combination of options that contains the most correct descriptions.
1 2 5 
3 4 5 
1 3 4 6 
1 3 5 8
1 2 4 6 7
4 5 6 8
1 4 6 8
包含正确描述最多的选项组合不止一个
Figure A and Figure B show that the structure has 4 $\rm Fe$ (green spheres) and 4 $\rm Si$ (silver spheres), and the projection represents all atoms of a unit cell. Therefore, the chemical formula is $\rm Fe_4Si_4$ within the unit cell, simplified to $\rm FeSi$

<Checkpoint>[The chemical formula is $\rm Fe_4Si_4$ within the unit cell, simplified to $\rm FeSi$](1)</Checkpoint>

In the $[111]$ direction projection of Figure B, the positions of the spheres do not have a center of symmetry relationship. Therefore, the structure as a whole has no center of symmetry.

<Checkpoint>[The structure as a whole has no center of symmetry](1)</Checkpoint>

A rotoinversion axis of order three contains a center of symmetry, so if there is no center of symmetry, there must be no rotoinversion axis of order three.

<Checkpoint>[If there is no center of symmetry, there must be no rotoinversion axis of order three](1)</Checkpoint>

Excluding the center of symmetry, the associated equivalent atoms in the $c$-axis projection can only be twofold axes, and the two atoms in the $a$-axis and $b$-axis directions are not directly opposite each other, so it can be determined that it is a $2_1$ screw axis.

<MultiModal>![$2_1$ screw axis position](/media/uploads/96d9f330-9477-4065-aafa-f3fc350a92b2.png)</MultiModal>

<Checkpoint>[$2_1$ screw axis exists](1)</Checkpoint>

The cubic crystal system point groups that do not contain a center of symmetry are only $T, O, T_d$, and as can be seen from Figure A, there is no fourfold axis in the $c$-axis direction, so it can only be the $T$ point group, and all numbers in the $T$ group are less than 210. In fact, this mineral is named Naqu mineral and belongs to the $P~2_1~3$ space group.

<Checkpoint>[There is no fourfold axis in the $c$-axis direction, so it can only be the $T$ point group](1)</Checkpoint>

<Checkpoint>[This mineral belongs to the $P~2_1~3$ space group](1)</Checkpoint>

The space group $P~2_1~3$ lacks two-fold rotation axes, possessing only $2_1$ screw axes. Consequently, the formation of a regular tetrahedron is impossible.

<Checkpoint>[4 identical atoms cannot form a regular tetrahedron](1)</Checkpoint>

Correct description is 1 4 6 8

<Checkpoint>[Correct description is 1 4 6 8](1)</Checkpoint>

The answer is G
图A和图B显示结构中有4个$\rm Fe$（绿色球）和4个$\rm Si$（银色球），且投影图代表一个晶胞的全部原子。因此化学式为单位晶胞内$\rm Fe_4Si_4$，简化为$\rm FeSi$

<Checkpoint>[化学式为单位晶胞内$\rm Fe_4Si_4$，简化为$\rm FeSi$](1)</Checkpoint>

图B的$[111]$方向投影中，球的位置不存在对称中心关系。因此结构整体无对称中心

<Checkpoint>[结构整体无对称中心](1)</Checkpoint>

三重反轴包含对称中心, 因此没有对称中心一定没有三重反轴

<Checkpoint>[没有对称中心一定没有三重反轴](1)</Checkpoint>

排除对称中心后, $c$轴投影图中关联等价的原子只能是二重轴, 且$a$轴与$b$轴方向上并两原子没有正对, 可以确定是$2_1$螺旋轴

<MultiModal>![$2_1$螺旋轴所在位置](/media/uploads/96d9f330-9477-4065-aafa-f3fc350a92b2.png)</MultiModal>

<Checkpoint>[存在$2_1$螺旋轴](1)</Checkpoint>

不包含对称中心的立方晶系点群仅有$T, O, T_d$, 而从图A中可以看出, $c$轴方向没有四重轴, 因此只能是$T$点群, 而$T$群所有编号均小于210. 实际上, 此矿物名为那曲矿属于$P~2_1~3$空间群

<Checkpoint>[$c$轴方向没有四重轴, 因此只能是$T$点群](1)</Checkpoint>

<Checkpoint>[此矿物属于$P~2_1~3$空间群](1)</Checkpoint>

$P~2_1~3$空间群没有二重旋转轴，只有$2_1$螺旋轴，因此不可能组成正四面体。

<Checkpoint>[4个相同原子无法组成正四面体](1)</Checkpoint>

正确描述为1 4 6 8

<Checkpoint>[正确描述为1 4 6 8](1)</Checkpoint>

答案为G