Features Extended

Most motions and planetary configurations (using the term broadly) of Solar System astro-bodies (i.e., Solar System objects) repeat themselves approximately if you wait long enough.
This allows prediction of those motions and planetary configurations that repeat just by knowing their repeat periods: i.e., this astro-body was here on the sky today, and so it will be here again X days days from now.
The Venus cycle is the full set of repeating motions and planetary configurations of Venus.
The Venus cycle period is the time period for Venus to return to the same location on the sky relative to the Sun and the fixed stars, and so is the repeat period for any of Venus motions and planetary configurations relative to the Sun and the fixed stars.
There are two elementary periods for the Venus cycle: the sidereal year = 365.256363004 days (J2000) of the Earth and the Venus synodic period = 583.92 days (circa J2000).
The sidereal year is the Earth's orbital period around the Solar System center of mass relative to observable universe (i.e., the Earth's orbital period in the celestial frame of the Solar System).
The synodic period of Solar System object is the time it takes to come back to the same position relative to the Sun as seen from the Earth.
Ideal Venus cycle period P_ven equals nP_sid=mP_syn, where
1. P_sid = sidereal year = 365.256363004 days (J2000).
2. P_syn = Venus synodic period = 583.92 days (circa J2000).
3. n and m are, respectively, integer numbers of sidereal years and Venus synodic periods, where the periods are exactly known rational numbers and n and m have NO common divisors.
If we knew n or m, we would know the ideal Venus cycle period P_ven.
But the ideal Venus cycle period P_ven does NOT exist since the sidereal year and the Venus synodic period are only known to within some uncertainty (which is of order the last one or two trailing significant figures they are specified to) and those values evolve slowly with Solar System evolution and are now, for relevant example, NOT exactly what they were in the days of ancient Babylonian astronomy (c.1830--c.60 BCE).
The practical Venus cycle period P_ven equals mP_syn which approximately equals nP_jul, where P_jul is the Julian year = 365.25 days (exact by definition) and P_syn is observed value (with only so many significant figures known) and n and m are conveniently small integers.
The Julian year is preferable to the sidereal year since it is an exact fixed value without an annoying long trailing decimal fraction, it almost the same as the sidereal year, and you can specify a correction from a count of Julian years in days.
Note "conveniently small" usually means integers less than ∼ 10 but it is a bit in the eye of the beholder.
The (practical) Venus cycle period P_ven is found by a search calculation reported below in Table: Venus Cycle Found by Count of Venus Synodic Periods.
From a count of Venus synodic periods, it is clear that smallest discrepancy in days between the count of Venus synodic periods and the count of an integer number of Julian years with conveniently small n and m values is for m = 5 Venus synodic periods and n = 8 Julian years. The discrepancy is -2.40 days from the exact count of n = 8 Julian years.
So the Venus synodic period can be conveniently set to 5 Venus synodic periods (2919.60 days) and 8 Julian years (2922 days).
```
Table:  Venus Cycle Found by Count of Venus Synodic Periods

Count  t (days)   t (Jyr)  t_r (Jyr)  δt (days)

  1     583.920     1.599      2      -146.580
  2    1167.840     3.197      3        72.090
  3    1751.760     4.796      5       -74.490
  4    2335.680     6.395      6       144.180
  5    2919.600     7.993      8        -2.400
  6    3503.520     9.592     10      -148.980
  7    4087.440    11.191     11        69.690
  8    4671.360    12.789     13       -76.890
  9    5255.280    14.388     14       141.780
 10    5839.200    15.987     16        -4.800
```
Note:
1. Count is the count of Venus synodic periods (each = 583.92 days (circa J2000))
2. t (days) is the time accumulated in the unit standard metric day = 24 h = 86400 s.
3. t (days) is the time accumulated in the unit Julian year = 365.25 days (exact by definition).
4. t_r (Jyr) is the rounded-to-integer value of t (days).
5. δt (days) = [t (days)] - [t_r (Jyr)]*[365.25 days].
What if you were super obssesive and wanted to know n and m integers with possibly a common divisor treating as exact to all trailing digits sidereal year = 365.256363004 days (J2000). and Venus synodic period = 583.92 days (circa J2000). The answer is
```
  n/m = 583.92/365.256363004 = (58392*10**7)365256363004  .
```
You would need a computer program to remove all common divisors. There is obviously at least one such: common divisor 2. Of course,
```
  n/m = 583.92/365.256363004 = 1.5986579814726057710 ≅ 8/5  .
```

File: Babylon file: venus_tablet_1bb.html.