Planet Figures

Astrology, planet figures or cosmic combinations

Dr. C.J. Krap, Alkmaar, the Netherlands

Download as pdf: astrology part 1 and astrology part 2

PART I

Inspired by Joan Negus, who wrote the book Cosmic Combinations,
I will explain an elegant way to predict symmetric planet figures. Based on the introduction of both the family score system and the outsider theory you may find them all.

The aspects used are: 30 – 36 – 45 – 60 – 72 – 90- 108 – 120 – 135 – 144 – 150 and 180 degrees. Aspect angles below 30 degrees are not frequently considered, but can easily be incorporated into the families.

The planet figures, I have studied, are split into four groups.

  • family of the trine                                                                 Δ
  • family of the square                                                             □︎
  • family of the quintile                                                           Q
  • structures outside the centre M of the horoscope

Each family has a specific set of aspects and a unique family score FS. An aspect, the angle between two planets and the centre M of the horoscope, is shown as a straight line in the circle. In the system I have developed every aspect is also connected to one of the following small numbers: 1. 2,3 …6. When the sum of corresponding aspect numbers equals FS a planet figure occurs. FS ensures that the sum of the aspects is 360 degrees, which is necessary to form a closed figure around the centre M of the horoscope. Most of them don’t have any symmetry like the very common triangle with the numbers 2 4 6 i.e. the triangle has three different sides (see below) but realise that the numbers represent angles and not the lengths of the sides. Starting with the 2 means that I have chosen to begin with the aspect below at the left side and then proceed clockwise. First, we will consider only the symmetric patterns who obey the family score rule. In the terminology of poker, for a triangle there must be three of a kind (aaa), which is the Grand Trine or one pair (aab) of aspects (which make them equilateral). Four of a kind (aaaa) is the Grand Cross and I will prove that in the case of squares two pair (aa and bb) and placed in the circle in the following order: abba is a kite and abab is a rectangle. A square with one pair (abac) or three of a kind (aaab) is a cradle. The figures with aspects in the following order aabc are not symmetric.

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I will show that symmetric pentagons are possible in limited numbers. The chance that a symmetric formation occurs in a horoscope rapidly decreases with increasing numbers of planets needed (no conjunctions of coarse). Therefore, combinations demanding six planets (hexagons) are very, very rare. They will occur, however, since there are billions of humans on earth. The hexagons will be dealt with in a second article which is being worked at.

Three colours are used for the aspects:

  • green            mild aspect
  • red                hard aspect
  • blue              aspect with mixed character

Maybe some astrologers want to use the 15 and 18 degree aspects. They correspond to the fraction ½ family score system. This means you have to use them twice otherwise the family score 12 or 10 can never be reached. There are only two cradles predicted (Δ and Q family) with two ½ aspects. The family score system predicts the presence of a planet figure and it’s shape. But I was surprised by the two opposition aspects at the bottom.

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All the other figures, containing these tiny aspects with very low orbs, are pentagons or hexagons, which (because of the small orbs and the large number of planets needed) have a very low probability to occur in a horoscope.
The moon nodes are in perfect opposition and as a consequence an aspect with one node is often accompanied with an aspect with the other node. For instance, sextile with a trine or semi-sextile with quincunx and so on. This property of the nodes ensures that they occur frequently in symmetric cosmic combinations.
It is well known that the aspects are generated by dividing 360 by 2,3,4 and 6. This results in 180, 120, 90 and 60, but dividing by 5 gives 72.
Many people think it is a number like 22 or 52, but students of math know better. For astrologers supporting Q and BQ as majeur aspects I have good news. The quintile family is large. Another sign that 72 is an important number.

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* The Mystic Rectangle was probably first found by Dane Rudhyar and is dealt with in the book Dynamics of aspect analysis by Bill Tierney.
Notice that: 3    3     6 is the T-square and 3    3    3    3 the Grand Cross both included in the square family. It may be surprising that the pentagons contain so many T-squares and other red lines.

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Outsiders
However, there are other figures that can’t be found using the family score system. They don’t have the centre of the horoscope inside. Another approach discovers these symmetric structures. For triangles take an aspect with a large angle. That’s the bottom of the triangle. Divide it into two equal parts and when the result is another aspect you have the sides to the top. To obtain the cradles split the angle into three parts, pentagons into four and there is also one hexagon possible. The smaller outsiders can be part of a larger structure (look for instance in the top of the kites), but they can also occur on their own.

Outsider formula
The sum of aspect numbers must be equal to the final number on the right.

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PART II
As promised in part one, the pictures of hexagons are dealt with in part two. In the world of astrologers a well known one is the Grand Sextile. Possibly, because it contains only major aspects.
All the others are loaded with one or more minor aspects.

Without proof, my guess is that the chance of finding such a hexagon with minors in a horoscope is much higher than that of the Grand Sextile.
My argument is that the abundance of the minor hexagon makes them more common. For readers who want to create an aspect family as an exercise, I have written a detailed example of how to perform such a challenge.
Complete new symmetric planet figures can be found nowadays in the presentations by several companies on the Internet. It may interest you to see the origin of these sometimes beautiful symmetric cosmic combinations.

Contents

  • hexagons of the trine and square families
  • hexagons of the Quintile family
  • an example of creating an aspect family
  • an exercise to create an aspect family yourself
  • symmetric planet figures created by distortion
  • answer to the exercise
  • hexagon formula numbers, summary and conclusion

I recommend reading part one first. It contains an explanation of the family score system FS, the outsider theory, all triangles, kites, rectangles, cradles and pentagons of the Δ, □ and Q families. In addition to another category of cosmic combinations: the outsiders.
Special thanks go to M. E. Wolters and L. S. Monté for their advice and help I received writing the two articles.

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A few polygons with more than six sides can be seen.
Heptagon I and octagon II are the only possible polygons of the square family with more than six sides. FS determines the maximum number of polygon sides in the families. For the trine family it is the dodecagon. The general rule is that the possibility to occur decreases with increasing numbers of the minor aspect 1.
So the heptagon (1 1 1 1 1 1 6) has a lower probability than (1 1 2 2 1 1 4).
There are plentiful heptagons of the trine family and the ones with the most important aspects are (2 2 1 1 2 2 2) (1 2 1 2 2 2 2) and (1 2 2 1 2 2 2).

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A description of how to create an aspect family. The Septile family.
I have chosen the rarely used Septile aspect with aspect angle S = 360° : 7.
Primarily, because the Septile family has some differences with the families of article part one and secondly as it demonstrates the power of the FS system.
S = 51.4285714285… degrees, a never ending story like pi (3.14…).
In the FS system S is reduced to 1.

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Exercise
The novile aspect N is not commonly used in astrology. It’s obtained by 360°:9 = 40° On the internet you may find several astrologers using it.
As it is relatively unknown it may be a good aspect to get used to the FS system and find the cosmic combinations of this family. The Novile family is a little more complicated than the example given before.
That’s mainly caused by the pentagons and hexagons.
When you like puzzles and astrology you may have some fun by solving this one.
The answer to the exercise is given at the end of this article.
You need some equipment from secondary school if you want to draw the pictures yourself before turning to the answer.

Symmetric planet figures created by distortion

Butterflies
Observe the cradle from the trine family with angles (90° 30° 90° 150°).
(3     1     3     5)

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If you don’t know that this cradle generates the butterflies, things may become very confusing. The only task that has to be done is to remove the semi-sextile (upper side) and the quincunx (lower side). This can be done by bending the aspect angles. Usual orbs are 2 for semi-sextile, 3 for quincunx, 8 for □ and Δ. With four aspects involved this could be a difficult mathematical problem. But it proves to be a case of logic.
The □ may vary between 82° and 98° and the upper angle between 17° – 43° with a gap of forbidden angles between 28° – 32°. Three butterflies can be seen on the next page. To the left you see one very close to the perfect cradle but distorted to (90° 34° 90° 146°) the others are more pushed to the limits (98° 18° 98° 146°) and (82° 42° 82° 154°).
There are many other possibilities, like mixed angles of □ but the result will be the same, a butterfly is born and the distorted cradle 3 1 3 5 is the mother of all butterflies.

I must admit that if colleague astrologers had not discovered the butterflies in a horoscope, I could have overlooked them easily.

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Telescopes, most of them are fakes.
The figure telescope can be found in some articles on the Internet.
Two small aspect are connected by red lines (oppositions).
Small aspect angles are 20°, 18° and 15°
(½ N. half semi-Quintile and half semi-sextile).
You find them below. And uh-uh the telescopes turn out to be rectangles.

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The long side 4N (160 degrees) is a major aspect of the Novile family.
The long side 4½Q (162 degrees) belongs to the Q family.
The 5½    (165 degrees) is called the tao aspect of the Δ family.
An acceptable orb for the ½ aspects is 1.
It’s obvious that the major aspect 4N can’t be neglected in favor of the minor ½ N to create a telescope and I don’t see why the orb of the 4½ and the 5½ (tao) long side aspects should be set to zero if you accept the ½ to be an aspect with orb 1.
Solution: draw rectangles.

Hour glasses
Hour glasses are related to the telescopes.
They are positioned upright and the aspect angles are larger.
You could try 30, 36, 40 , 60, 72, 80 and 90 degrees to create rectangles (which can be seen in articles one and two).
Now it’s somewhat different compared to the telescopes.

Six hour glasses can be created. Eradicate the aspect with the lowest orb by distortion as we have done to obtain the butterflies. The thin ones are obtained from 40, 72 and 80 degrees upper side angles and the broad ones from 150, 144 and 120. By distortion of the 90° the total figure collapses. Conclusion: hour glasses are figures with unperfect angles compared to the ones listed above. They need precise bending of the aspect angles and the margins to do so are very small compared to the butterflies but instead of that they have six possibilities that can occur. Hour glasses with upper sides 30° or 60° are weird, the left and right sides with the higher orbs are simply left out.

Six hour glasses can be created. Eradicate the aspect with the lowest orb by distortion as we have done to obtain the butterflies. The thin ones are obtained from 40, 72 and 80 degrees upper side angles and the broad ones from 150, 144 and 120. By distortion of the 90° the total figure collapses. Conclusion: hour glasses are figures with unperfect angles compared to the ones listed above. They need precise bending of the aspect angles and the margins to do so are very small compared to the butterflies but instead of that they have six possibilities that can occur. Hour glasses with upper sides 30° or 60° are weird, the left and right sides with the higher orbs are simply left out.

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The star
Six diagonals in the Grand Sextile form two Grand Trines. Keep the Grand Trine with the straight lines at place, then turn the dotted Grand Trine clockwise and after a few degrees say, about 5°, the sextiles (orb 4) disappear. Keep on turning about 55 degrees and between all those actions the stars seem to be born.

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In the Grand Sextile the two triangles are coupled to each other by the sextile aspects. In the star there is no connection at all. They must be considered as two independent Grand Trines. Also other complications arise (an example can be seen in the solution of the exercise).

Butterflies, hour glasses and stars have one thing in common
– they are twisted figures of perfect symmetric planet figures.
Maybe some day another beautiful shape is discovered which up to now has been unknown. Keep in mind that this new discovery most certainly is a distorted variety of a more complicated figure found by the FS system. I can already predict one.
The Mega Butterfly is created by distortion of the hexagon Δ.14.

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Answer to the exercise

  • The smallest aspect angle of the N family is 40 degrees
  • FS = 360 : 40 FS = 9
  • the aspects are a multiples of 40° (N). 40°  80°  120°  160°  200° 240°…
    Drop 200° 240° …
  • The aspect numbers for 40°  80°  120°  160° are: 1, 2 , 3 and 4.
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Trine aspects can be seen as green lines and some 2N and 4N diagonals can be seen in the pictures. Diagonals can easily be found by the aspect numbers. In case of the N family two neighbouring aspects 1 + 2 form a trine and 2 + 2 or 1 +3 the long diagonal 4. In the same way you can deduct the diagonals for other families, but in those figures I didn’t draw all diagonals either. A trine (aspect number 3) can be replaced by two sextiles (aspect number 1½).
The resulting possible symmetric planet figures are not presented in this article.

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In summary: the planet figures I have found are split into five families:

  • the trine and square families (Δ end □) used by most astrologers.
  • the Q, S and N families for those who want to experiment and leave the traditional path to find possible new insights in astrology.

In conclusion:
Using two astrological theories, the family score system and the outsider theory, it is possible to predict the existence of all symmetric planet figures.

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