This page contains examples of magic stars from
order12 to order14. Because there are multiple patterns for each order
there are a total of 14 different magic star examples.
The Magic Star Examples page shows the 14
patterns for orders 5 to 11.
Contents
Introduction...to magic stars 
Order12a...# 275 of >800,000 
Order12b...# 397,829 of >800,000 
Order12c...# 325 of >800,000 
Order12d...# 270,030 of >800,000 
Order13a...# 10 of >3,000,000 
Order13b...# 10 of >3,000,000 
Order13c...# 10 of >3,000,000 
Order13d...# 10 of >3,000,000 
Order13e...# 10 of >3,000,000 
Order14a...# 10 of >7,000,000? 
Order14b...# 10 of >7,000,000? 
Order14c...# 10 of >7,000,000? 
Order14d...# 10 of >7,000,000? 
Order14e...# 10 of >7,000,000? 
Example Magic Stars
Order12a

Order12 uses the consecutive numbers from 1 to 24
(2 x 12). Patterns A, B and C are noncontinuous, pattern D is
continuous.
Index # 475? of estimated 800,000+ basic solutions. Each line
sums to 50.
This pattern contains two superimposed hexagons (12 = 2 x 6). In
this case the corners of each hexagon sum to 60. In all cases the
corners of the two hexagons will sum to the same value.
The index number for most of these larger examples is uncertain
because not all of the solutions were found yet. 
Order12b

Index # 397,829 of 826,112 basic solutions. It's
points contain the numbers from 1 to 12.
Its complement is # 826112, the last basic solution in the list, and
obviously has the numbers 13 to 24 at the points.
This pattern contains three superimposed squares (12 = 3 x 4).
My 200 Mhz Pentium Pro, with 64 Megs of RAM took 39.5 days to
find the 826112 basic solutions. The data file size is 50 Megabytes. 
Order12c

Index # 325,000 of estimated 800,000+ basic
solutions. Each line sums to 50. This pattern contains four
superimposed triangles
(12 = 4 x 3). Their points sum to 30, 32, 34, 36.

Order12d

Index # 277030 of estimated 800,000+ basic
solutions. Each line sums to 50. This pattern is the only one of
four for this order that is continuous.

Order13a

Order13 uses the numbers from 1 to 26. Each of the
13 lines sums to 54. There are five different patterns in this
order and because 13 is a prime number, all 5 patterns are
continuous.
This is index #10 of more then 3,000,000 basic solutions for
order13a. 
Order13b

This is index #10 of more then 3,000,000 basic
solutions for order13b.

Order13c

This is index #10 of more then 3,000,000 basic
solutions for order13c. 
Order13d

This is index #10 of more then 3,000,000 basic
solutions for order13d. 
Order13e

This is index #10 of more then 3,000,000 basic
solutions for order13e

Order14a

Order14 uses the numbers from 1 to 28. Each of the
14 lines sums to 58. There are five different patterns in this
order. 3 of the patterns are noncontinuous, the other 2 are
continuous.
Pattern 14a is noncontinuous. It contains 2 septagons with the
points of each summing to the same value.
This is index #10 of more then 7,000,000? basic solutions for
order14a. 
Order14b

Pattern 14b is continuous. This is index #10 of
more then 7,000,000? basic solutions for order14b. 
Order14c

Pattern 14c is noncontinuous. It consists of 2 type
7A stars with the points of each summing to the same value. This
is index #10 of more then 7,000,000? basic solutions for order14c.

Order14d

This is index #2215000 of more then 7,000,000? basic
solutions for order14d. Total number of solutions
The numbers given for estimates of the number of basic solutions is
just that, an estimate. Because of the large number of solutions, it
is impossible to find them all in a reasonable time span. However,
time required varies directly with the number of consecutively names
points in the pattern. This pattern, with only 2 consecutive point
names (AA and BB), runs thousands of times faster then, say,
order14 patterns A, C and E with their 7 consecutive point names.
I started this run on Dec. 24/00 and by Feb. 10/01 had reached
solution # 2,215,000. The first number in the solution (cell A) is
still 1 and the 2nd number (cell B) now 14. Solution lists for the
smaller orders indicate that when the first number becomes a two,
approximately one half the solutions have been found. 
Order14e

Pattern 14d is a continuous pattern. Pattern 14e
is noncontinuous. It consists of 2 type 7B stars with the points of
each summing to the same value.
This is index #10 of more then 7,000,000? basic solutions for
order14e. 
