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一般矩阵：
(105b)
对应于绕原点的旋转，可能还结合了相对于通过原点O的平面的对称。
三维世界中的居民是三维结构。请记住，在三维欧几里得世界中并不存在时间。
在二维世界中存在方向性。之前我们展示了一个R与俄文字母“я”相交的情形。在三维中，其结果为：
(106)
(107)
(108)
(109)
右手和左手是否属于不同的物种？这取决于你选择的群。在三维空间中，你可以使用两个群。第一个是我们称之为“特殊欧几里得群”的群。(110)
你无法找到该群中的任何元素，其作用可以将右手变为左手，反之亦然。
但若使用完整的欧几里得群，则成为可能：
(111)
你会问：决定我今天生活的是哪一个群？
……在当今世界，我们看到各种物体。尤其是每天刮胡子时照镜子看到的自己影像。这时你有两个选择：
1 - 你决定镜子中的影像并非真实存在（尽管你每天都在使用它），那么你的几何世界就对应于第一个群。
2 - 你决定镜中另一侧所见的物体是真实的。
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那么你的世界就对应于第二个群。
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这将极大地扩展你平面世界的体积。
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尽快前往最近的精神病院。
原文（英文）
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The general matrix :
(105b)
corresponds to a rotation around the origin, eventually combined to a symmetry with respect to a plane which contains the origin O.
Inhabitants of a 3d's world are 3d structures. Remember times does not exist in 3d Euclid's world.
Orientation exists in 2d worlds. Above we presented a R meeting a russian "ia" letter. In 3d, it gives :
(106)
(107)
(108)
(109)
Do a right and a left hand belong to distinct species . Depends on the group you choose. In 3d you can use two groups. The first is what we called the Special Euclid's group. (110)
You can't find any element of this group whose action can transform a right and into a left and, and vice-versa.
But it becomes possible with the complete Euclid's group :
(111)
You will say : what is the group that runs my today's life ?
...In today's world we see different objects. In particular our image in a looking glass, when shaving, each morning. Then we have two choices:
1 - You decide that your image in the looking glass is a not real (although you use it daily) so that you geometrical world corresponds to the first group.
2 - You decide the object you see on the other side of you mirrors are real.
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Then your wold corresponds to the second group.
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It increases drastically the volume of your flat.
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Join a psychiatric hospital as fas as you can.