* Magic cube with Gaudi's square

 
Magic cube 4x4x4 composed with 12 magic squares, including the one of Gaudi:
  
Antoni Gaudí (1852-1926), was a Catalan architect. In one of his major creations, the Sagrada Familia cathedral in Barcelona, he used the following magic square, among many other symbolic and decorative element:
 
 
The magic constant is 33, probably referring to the commonly accepted age of Christ'a death. This magic square is singular, in the sense that it includes the numbers 10 and 14 twice . However, it complies with the same construction rules as Dürer's magic square. The magic constant shows up in many combinations (diagonals, 4 corners, 4 central cells, ...).
 
According to my method, it is thus very simple to include this square into a magic cube, the same way I used with Dürer's magic square (you may download the Excel file at the bottom of this page):
 

 

Each magic square included in the thus built cube, gives the sum of 33 on every row and every column.

The addition of the elements of each pillar of the cube (e.g. the upper left corners of the squares: 1 - 2 - 7 + 41), always produces the magic constant of 33.

Because of duplicates (the 10 and the 14) in Gaudi's magic square, the cube contains the maximum possible of 62 different numbers.

 

 

 

Gaudi's magic square (upper face)

1

14

14

4

11

7

6

9

8

10

10

5

13

2

3

15

 

second level (under Gaudi's square)

-2

-13

18

 30

 31

-16

44

-26

 26

22 

-9 

-6

-22

40 

-20

 35

 

 

third level

-7

55

-35

20

-32

17

-12

60

16

-31

59

-11

56

-8

21

-36

 

fourth level (bottom side of the cube)

41

-23

36

-21

23

25

-5

-10

-17

32

-27

45

-14

-1

29

19

Dürer and Gaudi magic cubes built according to this method, probably have an infinity of solutions.
 
Ĉ
Ali Skalli,
Oct 14, 2009, 9:10 AM
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