ANSWER: There are actually TWO Old Testament scriptures that refer to this vision of Ezekiel.
The appearance of the wheels and their workings was like the color of beryl, and all four had the same likeness. The appearance of their workings was, as it were, "A WHEEL IN THE MIDDLE OF A WHEEL" (Ezekiel 1:15 - 16)
And when I looked, there were four wheels by the cherubim, one wheel by one cherub and another wheel by each other cherub . . . (Ezekiel 10:9)
Of the many fascinating scriptural descriptions of heavenly things in Ezekiel's vision, this one of chapters 1 and 10 is by far the most stunning and complex. The description itself is hard enough for us to understand since there is nothing similar to it in the Bible nor are we told what to compare these descriptions to so that we may understand them. The prophet had to describe in the Hebrew language what he saw, which was so incredible and foreign to his experiences as a human. The difficulty of understanding these scriptures (or any others) is that the translation of the texts from Hebrew to English is sometimes not easy nor perfect.
Since there is no certain and crystal clear understanding of this subject simply by reading the text, (if someone has it please share it with us), even after consulting Bible commentaries we can only come to an imperfect, general understanding. The Apostle Paul explained our limited vision and understanding of spiritual things.
"For now we see in a mirror, dimly, but then face to face. Now I know in part, but then I shall know just as I also am known." (1Corinthians 13:12)
In Ezekiel 1:1, we are introduced to "visions of God." Verse 4 describes the startling sight of a whirlwind with a raging fire having great brightness. Verses 5 to 15 describes the four Cherubim, each having four faces (one on each side). These powerful spirit beings were like fire in appearance with lightning emanating from them. The following description is from an old Abingdon Bible Commentary.
"The description is full of the splendor of flashing light, so brilliant that the details are minutely revealed, but so dazzling that they are not clearly seen . . . Textual corruption, which do not seriously affect the general interpretation, have aggravated the obscurity in some points of detail"
Next to each Cherub one wheel was place next to another one. A few Bible commentaries state that the wheels traversed each other (one inside another). Like in a cross, they allowed the spirits to immediately go in any of four directions where they were told to go (verses 16, 17). In regard to how the wheels were engineered, our limited understanding makes its almost impossible to comprehend how such things would be made supernaturally.
The JFB Commentary offers the below explanation.
". . . each wheel was composed of two circles cutting one another at right angles"
There are two more facets that are described. One facet is the "rings were full of eyes" (verse 18). Since men's eyes are for seeing, and man is made in the likeness of God (Genesis 1:26), we can safely assume that they are meant for the same. The great number of eyes on the rings may portend or symbolize how great is God's awareness and direction of events. The second facet was dreadful and high rings (verse 18). It isn't clear whether, in regard to its shape, it means the ring depth or the large spoke size. In either case, it surely would surpass any of Hollywood's "special effects", only that this is very real, even as unseen to us today.
Some commentaries indulge in various allusions on this subject that is merely speculative and unsubstantiated by the Bible. The Scriptures are not for "private interpretation" (1Peter 1:20). We need to be satisfied with what God allows us to comprehend about the wheel vision given to Ezekiel.