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A good illustration is [[water|H₂O]], one atom of hydrogen and two atoms of oxygen. It can also take three forms: solid ice, liquid water, and floating clouds, steam, formless fog and invisible vapor, all of which are considered water. However, this [[analogy]] was historically taken too far as applied to God. The denial of the doctrine of the Trinity, as being in essence one Person only, not three divine Persons of One Being, was condemned as [[Monarchianism]] and as [[Modalism]] and as the [[heresy]] of Sabellianism<ref>[https://orthodoxwiki.org/Sabellianism '''Sabellianism''' (orthodoxwiki.org)]</ref>

A good illustration is [[water|H₂O]], one atom of hydrogen and two atoms of oxygen. It can also take three forms: solid ice, liquid water, and floating clouds, steam, formless fog and invisible vapor, all of which are considered water. However, this [[analogy]] was historically taken too far as applied to God. The denial of the doctrine of the Trinity, as being in essence one Person only, not three divine Persons of One Being, was condemned as [[Monarchianism]] and as [[Modalism]] and as the [[heresy]] of Sabellianism<ref>[https://orthodoxwiki.org/Sabellianism '''Sabellianism''' (orthodoxwiki.org)]</ref>

An excellent [[Mathematics|mathematical]] illustration of the unity of the Trinity is the [[Geometry|geometrical]] form of the [[Triangle|triangular]] three-sided ''[[tetrahedron]]'', a [[Pyramid (geometry)|pyramidal]] construct of a single, indivisible point extending into three [[equilateral]] triangular faces simultaneously united to a single triangular base<ref>[https://www.mathsisfun.com/geometry/tetrahedron.html tetrahedron (mathsisfun.com)]</ref>. This is especially evident when an equilateral tetrahedron is made of flawless transparent [[crystal]]. Through any one face of the crystal form each of the other sides is clearly visible. Each of the faces is a distinctly different face (they cannot be the same face) but all of them have exactly the same shape, the same size, and the same substance. What is predicated of any one of them is predicated of each of them. A tetrahedral crystal displayed standing on the flat surface of the jeweler's counter or the shelf of a display case cannot exist without three faces inseparably existing as extending from the single, undivided point of one apex to the same undivided triangular base at its base or foundation on which it stands: a single crystal, not three, with three faces, not one. No matter how it is turned or rotated, it always looks the same and remains the same.

An excellent [[Mathematics|mathematical]] illustration of the unity of the Trinity is the [[Geometry|geometrical]] form of the [[Triangle|triangular]] three-sided ''[[tetrahedron]]'', a [[Pyramid (geometry)|pyramidal]] construct of a single, indivisible point extending into three [[equilateral]] triangular faces simultaneously united to a single triangular base<ref>[https://www.mathsisfun.com/geometry/tetrahedron.html tetrahedron (mathsisfun.com)]</ref>. This is especially evident when an equilateral tetrahedron is made of flawless transparent [[crystal]]. Through any one face of the crystal form each of the other sides is clearly visible. Each of the faces is a distinctly different face (they cannot be the same face) but all of them have exactly the same shape, the same size, and the same substance. What is predicated of any one of them is predicated of each of them. A tetrahedral crystal displayed standing on the flat surface of the jeweler's counter or the shelf of a display case cannot exist without three faces inseparably existing as extending from the single, undivided point of one apex to the same undivided triangular base at its surface or foundation on which it stands: a single crystal, not three, with three faces, not one. No matter how it is turned or rotated, it always looks the same and remains the same.

And just as a tetrahedron has a stable vertical configuration because of its [[Triangle|triangular]] base, likewise, any large object, or sturdy, movable, stationary, horizontal supportive platform, which stands firmly on uneven, basically level ground, with an equilateral triangular base of three equidistant points of contact, legs or feet (where a [[square]] base of four equidistant points of contact with uneven ground can wobble or tilt), having a measurable height not more than its width, and an upper structure or surface not extending its outward edges beyond bounds more broad or extensive than its base, has the most stable physical configuration, with a stable center of gravity, and the most reliable safety for those on such a platform, who depend on its help to stand securely without any danger of falling.

And just as a tetrahedron has a stable vertical configuration because of its [[Triangle|triangular]] base, likewise, any large object, or sturdy, movable, stationary, horizontal supportive platform, which stands firmly on uneven, basically level ground, with an equilateral triangular base of three equidistant points of contact, legs or feet (where a [[square]] base of four equidistant points of contact with uneven ground can wobble or tilt), having a measurable height not more than its width, and an upper structure or surface not extending its outward edges beyond bounds more broad or extensive than its base, has the most stable physical configuration, with a stable center of gravity, and the most reliable safety for those on such a platform, who depend on its help to stand securely without any danger of falling.