The ADOMAH Periodic Table
This is a profound and powerful way to visualize the periodic table of the elements – due to the fact that it mirrors 3-D physical reality:
Geometry of the Periodic Table.
It can be observed that four blocks of ADOMAH Periodic Table, that is built strictly in accordance with the quantum numbers n, l, ml and ms, follow quite curious rule: perimeters of all blocks are equal to 18 units (if elements are placed in rectangular boxes so that any given pair of elements fits in one unit square, see“Description” page): or
s-block is 1 unit high and 8 units long (or wide) (1+8 = 9, is half of the perimeter);
p-block is 3 units high and 6 units long (3+6 = 9);
d-block is 5 units high and 4 units long (5+4 = 9);
f-block is 7 units high and 2 units long (7 +2 = 9);
Therefore, perimeter of each block: P=2×9=18 units.
Those are only four possible rectangles that could have perimeter of 18, if only natural numbers are used. What can it possibly mean? Can it be a coincidence?
Apparently not, this is not a coincidence. In 3D world there is one geometric shape that, if sliced in a certain way, would produce rectangles with the same proportions, orientation, alignment and order as spdf blocks of ADOMAH Periodic Table. This shape is Regular Tetrahedron!
If a regular tetrahedron with edge E is intersected by a plane that is parallel to two opposite edges, cross section will always be a rectangle or a square with perimeter P=2E.
Proportions of fdps blocks of ADOMAH PT, as well as their sequence, alignment and orientation, suggest only one possible conclusion: all four blocks of the Periodic Table are consecutive slices of Regular Tetrahedron, with edges equal to 9 units, produced by the planes spaced 2 units apart, as measured along the edges.
There is another indication that the Periodic System has something to do with regular tetrahedron: Atomic Number of every other alkaline earth element (Be, Ca, Ba, Ubn…) corresponds to every second Tetrahedral Number: 1, 4, 10, 20, 35, 56, 84, 120… Remaining alkaline earth elements (Mg, Sr and Ra) have atomic numbers that are equidistant between the Tetrahedral Numbers shown above in bold: 12=(4+20)/2, 38=(20+56)/2, 88=(56+120)/2. See more on this topic below.
Generally, a Periodic System of any size can be described in terms of a regular tetrahedron with edge E:
1) number of the periods NOP=E-1;
2) number of values of the quantum number ‘n’: n max=E-1
3) number of blocks representing subshells (number of values of ‘l’): NOS=ceil(0.5(E-1)), where ceil stands for “ceiling function”, that means “rounded to a higher integer if the result has fractional part” (in case of even ‘E’).
4) maximum value of quantum number ‘l’: l max=ceil(0.5(E-3))
5) dimensions of the subshell blocks corresponding to l =0,1…, l max:
as measured along the periods a=4l +2 elements; as measured along the groups b=E-(2l +1).
6) number of elements in each block corresponding to quantum number l =0,1…, l max:
7) length of the periods: LP=2(l’ +1)2 ( here, l’ is the maximum value of l for each period).
8) number of the elements (NOE) in the periodic system that corresponds to the tetrahedron with edge ‘E’:
, where lmax=ceil(0.5(E-3)) as defined above.