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1, 2, 3, 4, 5, 8, 12, 16, 20, 60 more…  
The duodecimal system (also known as base12 or dozenal) is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A' or 'X', and the number eleven as 'B' or 'E' (another common notation, introduced by Sir Isaac Pitman, is to use a rotated '2' for ten and a reversed '3' for eleven). The number twelve (that is, the number written as '12' in the base ten numerical system) is instead written as '10' in duodecimal (meaning "1 dozen and 0 units", instead of "1 ten and 0 units"), whereas the digit string '12' means "1 dozen and 2 units" (i.e. the same number that in decimal is written as '14'). Similarly, in duodecimal '100' means "1 gross", '1000' means "1 great gross", and '0.1' means "1 twelfth" (instead of their decimal meanings "1 hundred", "1 thousand", and "1 tenth").
The number twelve, a highly composite number, is the smallest number with four nontrivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range. As a result of this increased factorability of the radix and its divisibility by a wide range of the most elemental numbers (whereas ten has only two nontrivial factors: 2 and 5, with neither 3 nor 4), duodecimal representations fit more easily than decimal ones into many common patterns, as evidenced by the higher regularity observable in the duodecimal multiplication table. Of its factors, 2 and 3 are prime, which means the reciprocals of all 3smooth numbers (such as 2, 3, 4, 6, 8, 9...) have a terminating representation in duodecimal. In particular, the five most elementary fractions (^{1}⁄_{2}, ^{1}⁄_{3}, ^{2}⁄_{3}, ^{1}⁄_{4} and ^{3}⁄_{4}), all have a short terminating representation in duodecimal (0.6, 0.4, 0.8, 0.3 and 0.9, respectively), and twelve is the smallest radix with this feature (since it is the least common multiple of 3 and 4). This all makes it a more convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary, octal and hexadecimal systems, although the sexagesimal system (where the reciprocals of all 5smooth numbers terminate) does better in this respect (but at the cost of an unwieldily large multiplication table).
Contents 
Languages using duodecimal number systems are uncommon. Languages in the Nigerian Middle Belt such as Janji, GbiriNiragu (Kahugu), the Nimbia dialect of Gwandara^{[1]}; the Chepang language of Nepal^{[2]} and the Mahl language of Minicoy Island in India are known to use duodecimal numerals. In fiction, J. R. R. Tolkien's Elvish languages used duodecimal.
Germanic languages have special words for 11 and 12, such as eleven and twelve in English, which are often misinterpreted as vestiges of a duodecimal system. However, they are considered to come from ProtoGermanic *ainlif and *twalif (respectively one left and two left), both of which were decimal.
Historically, units of time in many civilizations are duodecimal. There are twelve signs of the zodiac, twelve months in a year, and twelve European hours in a day or night. Traditional Chinese calendars, clocks, and compasses are based on the twelve Earthly Branches.
Being a versatile denominator in fractions may explain why we have 12 inches in an imperial foot, 12 ounces in a troy pound, 12 old British pence in a shilling, 12 items in a dozen, 12 dozens in a gross (144, square of 12), 12 gross in a great gross (1728, cube of 12), 24 (12 * 2) hours in a day, etc. The Romans used a fraction system based on 12, including the uncia which became both the English words ounce and inch. Predecimalisation, the United Kingdom and Republic of Ireland used a mixed duodecimalvigesimal currency system (12 pence = 1 shilling, 20 shillings or 240 pence to the pound sterling or Irish pound), and Charlemagne established a monetary system that also had a mixed base of twelve and twenty, the remnants of which persist in many places.
In a duodecimal place system, ten can be written as A, eleven can be written as B, and twelve is written as 10. For alternative symbols, see the section "Advocacy and 'dozenalism'" below.
According to this notation, duodecimal 50 expresses the same quantity as decimal 60 (= five times twelve), duodecimal 60 is equivalent to decimal 72 (= six times twelve = half a gross), duodecimal 100 has the same value as decimal 144 (= twelve times twelve = one gross), etc.
1  2  3  4  5  6  7  8  9  A  B  10 

2  4  6  8  A  10  12  14  16  18  1A  20 
3  6  9  10  13  16  19  20  23  26  29  30 
4  8  10  14  18  20  24  28  30  34  38  40 
5  A  13  18  21  26  2B  34  39  42  47  50 
6  10  16  20  26  30  36  40  46  50  56  60 
7  12  19  24  2B  36  41  48  53  5A  65  70 
8  14  20  28  34  40  48  54  60  68  74  80 
9  16  23  30  39  46  53  60  69  76  83  90 
A  18  26  34  42  50  5A  68  76  84  92  A0 
B  1A  29  38  47  56  65  74  83  92  A1  B0 
10  20  30  40  50  60  70  80  90  A0  B0  100 
The number 12 has six factors, which are 1, 2, 3, 4, 6, and 12, of which 2 and 3 are prime. The decimal system has only four factors, which are 1, 2, 5, and 10; of which 2 and 5 are prime. Vigesimal adds two factors to those of ten, namely 4 and 20, but no additional prime factor. Although twenty has 6 factors, 2 of them prime, similarly to twelve, it is also a much larger base (i.e., the digit set and the multiplication table are much larger) and prime factor 5, being less common in the prime factorization of numbers, is arguably less useful than prime factor 3. Binary has only two factors, 1 and 2, the latter being prime. Hexadecimal has five factors, adding 4, 8 and 16 to those of 2, but no additional prime. Trigesimal is the smallest system that has three different prime factors (all of the three smallest primes: 2, 3 and 5) and it has eight factors in total (1, 2, 3, 5, 6, 10, 15, and 30). Sexagesimal  which the ancient Sumerians and Babylonians among others actually used  adds the four convenient factors 4, 12, 20, and 60 to this but no new prime factors.
To convert numbers between bases, one can use the general conversion algorithm (see the relevant section under positional notation). Alternatively, one can use digitconversion tables. The ones provided below can be used to convert any dozenal number between 0.01 and BBB,BBB.BB to decimal, or any decimal number between 0.01 and 999,999.99 to dozenal. To use them, we first decompose the given number into a sum of numbers with only one significant digit each. For example:
123,456.78 = 100,000 + 20,000 + 3,000 + 400 + 50 + 6 + 0.7 + 0.08
This decomposition works the same no matter what base the number is expressed in. Just isolate each nonzero digit, padding them with as many zeros as necessary to preserve their respective place values. If the digits in the given number include zeroes (for example, 102,304.05), these are, of course, left out in the digit decomposition (102,304.05 = 100,000 + 2,000 + 300 + 4 + 0.05). Then we use the digit conversion tables to obtain the equivalent value in the target base for each digit. If the given number is in dozenal and the target base is decimal, we get:
(dozenal) 100,000 + 20,000 + 3,000 + 400 + 50 + 6 + 0.7 + 0.08 = (decimal) 248,832 + 41,472 + 5,184 + 576 + 60 + 6 + 0.583333333333... + 0.055555555555...
Now, since the summands are already converted to base ten, we use the usual decimal arithmetic to perform the addition and recompose the number, arriving at the conversion result:
Dozenal > Decimal 100,000 = 248,832 20,000 = 41,472 3,000 = 5,184 400 = 576 50 = 60 + 6 = + 6 0.7 = 0.583333333333... 0.08 = 0.055555555555...  123,456.78 = 296,130.638888888888...
That is, (dozenal) 123,456.78 equals (decimal) 296,130.638888888888... ≈ 296,130.64
If the given number is in decimal and the target base is dozenal, the method is basically same. Using the digit conversion tables:
(decimal) 100,000 + 20,000 + 3,000 + 400 + 50 + 6 + 0.7 + 0.08 = (dozenal) 49,A54 + B,6A8 + 1,8A0 + 294 + 42 + 6 + 0.849724972497249724972497... + 0.0B62A68781B05915343A0B62...
However, in order to do this sum and recompose the number, we now have to use the addition tables for dozenal, instead of the addition tables for decimal most people are already familiar with, because the summands are now in base twelve and so the arithmetic with them has to be in dozenal as well. In decimal, 6 + 6 equals 12, but in dozenal it equals 10; so if we used decimal arithmetic with dozenal numbers we would arrive at an incorrect result. Doing the arithmetic properly in dozenal, we get the result:
Decimal > Dozenal 100,000 = 49,A54 20,000 = B,6A8 3,000 = 1,8A0 400 = 294 50 = 42 + 6 = + 6 0.7 = 0.849724972497249724972497... 0.08 = 0.0B62A68781B05915343A0B62...  123,456.78 = 5B,540.943A0B62A68781B05915343A...
That is, (decimal) 123,456.78 equals (dozenal) 5B,540.943A0B62A68781B05915343A... ≈ 5B,540.94
Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec. 
100,000  248,832  10,000  20,736  1,000  1,728  100  144  10  12  1  1  0.1  0.083  0.01  0.00694 
200,000  497,664  20,000  41,472  2,000  3,456  200  288  20  24  2  2  0.2  0.16  0.02  0.0138 
300,000  746,496  30,000  62,208  3,000  5,184  300  432  30  36  3  3  0.3  0.25  0.03  0.02083 
400,000  995,328  40,000  82,944  4,000  6,912  400  576  40  48  4  4  0.4  0.3  0.04  0.027 
500,000  1,244,160  50,000  103,680  5,000  8,640  500  720  50  60  5  5  0.5  0.416  0.05  0.03472 
600,000  1,492,992  60,000  124,416  6,000  10,368  600  864  60  72  6  6  0.6  0.5  0.06  0.0416 
700,000  1,741,824  70,000  145,152  7,000  12,096  700  1008  70  84  7  7  0.7  0.583  0.07  0.04861 
800,000  1,990,656  80,000  165,888  8,000  13,824  800  1152  80  96  8  8  0.8  0.6  0.08  0.05 
900,000  2,239,488  90,000  186,624  9,000  15,552  900  1,296  90  108  9  9  0.9  0.75  0.09  0.0625 
A00,000  2,488,320  A0,000  207,360  A,000  17,280  A00  1,440  A0  120  A  10  0.A  0.83  0.0A  0.0694 
B00,000  2,737,152  B0,000  228,096  B,000  19,008  B00  1,584  B0  132  B  11  0.B  0.916  0.0B  0.07638 
Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz. 
100,000  49,A54  10,000  5,954  1,000  6B4  100  84  10  A  1  1  0.1  0.12497  0.01  0.015343A0B62A68781B059 
200,000  97,8A8  20,000  B,6A8  2,000  1,1A8  200  148  20  18  2  2  0.2  0.2497  0.02  0.02A68781B05915343A0B6 
300,000  125,740  30,000  15,440  3,000  1,8A0  300  210  30  26  3  3  0.3  0.37249  0.03  0.043A0B62A68781B059153 
400,000  173,594  40,000  1B,194  4,000  2,394  400  294  40  34  4  4  0.4  0.4972  0.04  0.05915343A0B62A68781B0 
500,000  201,428  50,000  24,B28  5,000  2,A88  500  358  50  42  5  5  0.5  0.6  0.05  0.07249 
600,000  24B,280  60,000  2A,880  6,000  3,580  600  420  60  50  6  6  0.6  0.7249  0.06  0.08781B05915343A0B62A6 
700,000  299,114  70,000  34,614  7,000  4,074  700  4A4  70  5A  7  7  0.7  0.84972  0.07  0.0A0B62A68781B05915343 
800,000  326,B68  80,000  3A,368  8,000  4,768  800  568  80  68  8  8  0.8  0.9724  0.08  0.0B62A68781B05915343A 
900,000  374,A00  90,000  44,100  9,000  5,260  900  630  90  76  9  9  0.9  0.A9724  0.09  0.10B62A68781B05915343A 
Exponent  Powers of 2  Powers of 3  Powers of 4  Powers of 5  Powers of 6  Powers of 7  
Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  
^6  64  54  729  509  4,096  2454  15,625  9,061  46,656  23,000  117,649  58,101 
^5  32  28  243  183  1,024  714  3,125  1,985  7,776  4,600  16,807  9,887 
^4  16  14  81  69  256  194  625  441  1,296  900  2,401  1,481 
^3  8  8  27  23  64  54  125  A5  216  160  343  247 
^2  4  4  9  9  16  14  25  21  36  30  49  41 
^1  2  2  3  3  4  4  5  5  6  6  7  7 
^−1  0.5  0.6  0.3  0.4  0.25  0.3  0.2  0.2497  0.16  0.2  0.142857  0.186A35 
^−2  0.25  0.3  0.1  0.14  0.0625  0.09  0.04  0.05915343A0 B62A68781B 
0.027  0.04  0.0204081632653 06122448979591 836734693877551 
0.02B322547A05A 644A9380B908996 741B615771283B 
Exponent  Powers of 8  Powers of 9  Powers of 10  Powers of 11  Powers of 12  
Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  Dec.  Doz.  
^6  262,144  107,854  531,441  217,669  1,000,000  402,854  1,771,561  715,261  2,985,984  1,000,000 
^5  32,768  16,B68  59,049  2A,209  100,000  49,A54  161,051  79,24B  248,832  100,000 
^4  4,096  2,454  6,561  3,969  10,000  5,954  14,641  8,581  20,736  10,000 
^3  512  368  729  509  1,000  6B4  1,331  92B  1,728  1,000 
^2  64  54  81  69  100  84  121  A1  144  100 
^1  8  8  9  9  10  A  11  B  12  10 
^−1  0.125  0.16  0.1  0.14  0.1  0.12497  0.09  0.1  0.083  0.1 
^−2  0.015625  0.023  0.012345679  0.0194  0.01  0.015343A0B6 2A68781B059 
0.00826446280 99173553719 
0.0123456789B  0.00694  0.01 
Duodecimal fractions may be simple:
or complicated
Examples in duodecimal  Decimal equivalent 
1 × (5 / 8) = 0.76  1 × (5 / 8) = 0.625 
100 × (5 / 8) = 76  144 × (5 / 8) = 90 
576 / 9 = 76  810 / 9 = 90 
400 / 9 = 54  576 / 9 = 64 
1A.6 + 7.6 = 26  22.5 + 7.5 = 30 
As explained in recurring decimals, whenever an irreducible fraction is written in radix point notation in any base, the fraction can be expressed exactly (terminates) if and only if all the prime factors of its denominator are also prime factors of the base. Thus, in baseten (= 2×5) system, fractions whose denominators are made up solely of multiples of 2 and 5 terminate: ¹⁄_{8} = ¹⁄_{(2×2×2)}, ¹⁄_{20} = ¹⁄_{(2×2×5)}, and ¹⁄_{500} = ¹⁄_{(2×2×5×5×5)} can be expressed exactly as 0.125, 0.05, and 0.002 respectively. ¹⁄_{3} and ¹⁄_{7}, however, recur (0.333... and 0.142857142857...). In the duodecimal (= 2×2×3) system, ¹⁄_{8} is exact; ¹⁄_{20} and ¹⁄_{500} recur because they include 5 as a factor; ¹⁄_{3} is exact; and ¹⁄_{7} recurs, just as it does in decimal.
Arguably, factors of 3 are more commonly encountered in reallife division problems than factors of 5 (or would be, were it not for the decimal system having influenced most cultures). Thus, in practical applications, the nuisance of recurring decimals is encountered less often when duodecimal notation is used. Advocates of duodecimal systems argue that this is particularly true of financial calculations, in which the twelve months of the year often enter into calculations.
However, when recurring fractions do occur in duodecimal notation, they are less likely to have a very short period than in decimal notation, because 12 (twelve) is between two prime numbers, 11 (eleven) and 13 (thirteen), whereas ten is adjacent to composite number 9. Nonetheless, having a shorter or longer period doesn't help the main inconvenience that one does not get a finite representation for such fractions in the given base (so rounding, which introduces inexactitude, is necessary to handle them in calculations), and overall one is more likely to have to deal with infinite recurring digits when fractions are expressed in decimal than in duodecimal, because one out of every three consecutive numbers contains the prime factor 3 in its factorization, while only one out of every five contains the prime factor 5. All other prime factors, except 2, are not shared by either ten or twelve, so they do not influence the relative likeliness of encountering recurring digits (any irreducible fraction that contains any of these other factors in its denominator will recur in either base). Also, the prime factor 2 appears twice in the factorization of twelve, while only once in the factorization of ten; which means that most fractions whose denominators are powers of two will have a shorter, more convenient terminating representation in dozenal than in decimal (e.g., 1/(2^{2}) = 0.25 dec = 0.3 doz; 1/(2^{3}) = 0.125 dec = 0.16 doz; 1/(2^{4}) = 0.0625 dec = 0.09 doz; 1/(2^{5}) = 0.03125 dec = 0.046 doz; etc.).
Decimal base Prime factors of the base: 2, 5 
Duodecimal / Dozenal base Prime factors of the base: 2, 3 

Fraction  Prime factors of the denominator 
Positional representation  Positional representation  Prime factors of the denominator 
Fraction 
1/2  2  0.5  0.6  2  1/2 
1/3  3  0.3333... = 0.3  0.4  3  1/3 
1/4  2  0.25  0.3  2  1/4 
1/5  5  0.2  0.24972497... = 0.2497  5  1/5 
1/6  2, 3  0.16  0.2  2, 3  1/6 
1/7  7  0.142857  0.186A35  7  1/7 
1/8  2  0.125  0.16  2  1/8 
1/9  3  0.1  0.14  3  1/9 
1/10  2, 5  0.1  0.12497  2, 5  1/A 
1/11  11  0.09  0.1  B  1/B 
1/12  2, 3  0.083  0.1  2, 3  1/10 
1/13  13  0.076923  0.0B  11  1/11 
1/14  2, 7  0.0714285  0.0A35186  2, 7  1/12 
1/15  3, 5  0.06  0.09724  3, 5  1/13 
1/16  2  0.0625  0.09  2  1/14 
1/17  17  0.0588235294117647  0.08579214B36429A7  15  1/15 
1/18  2, 3  0.05  0.08  2, 3  1/16 
1/19  19  0.052631578947368421  0.076B45  17  1/17 
1/20  2, 5  0.05  0.07249  2, 5  1/18 
1/21  3, 7  0.047619  0.06A3518  3, 7  1/19 
1/22  2, 11  0.045  0.06  2, B  1/1A 
1/23  23  0.0434782608695652173913  0.06316948421  1B  1/1B 
1/24  2, 3  0.0416  0.06  2, 3  1/20 
1/25  5  0.04  0.05915343A0B62A68781B  5  1/21 
1/26  2, 13  0.0384615  0.056  2, 11  1/22 
1/27  3  0.037  0.054  3  1/23 
1/28  2, 7  0.03571428  0.05186A3  2, 7  1/24 
1/29  29  0.0344827586206896551724137931  0.04B7  25  1/25 
1/30  2, 3, 5  0.03  0.04972  2, 3, 5  1/26 
1/31  31  0.032258064516129  0.0478AA093598166B74311B28623A55  27  1/27 
1/32  2  0.03125  0.046  2  1/28 
1/33  3, 11  0.03  0.04  3, B  1/29 
1/34  2, 17  0.02941176470588235  0.0429A708579214B36  2, 15  1/2A 
1/35  5, 7  0.0285714  0.0414559B3931  5, 7  1/2B 
1/36  2, 3  0.027  0.04  2, 3  1/30 
As for irrational numbers, none of them has a finite representation in any of the rationalbased positional number systems (such as the decimal and duodecimal ones); this is because a rationalbased positional number system is essentially nothing but a way of expressing quantities as a sum of fractions whose denominators are powers of the base, and by definition no finite sum of rational numbers can ever result in an irrational number. For example, 123.456 = 1 × 1/10^{2} + 2 × 1/10^{1} + 3 × 1/10^{0} + 4 × 1/10^{1} + 5 × 1/10^{2} + 6 × 1/10^{3} (this is also the reason why fractions that contain prime factors in their denominator not in common with those of the base do not have a terminating representation in that base). Moreover, the infinite series of digits of an irrational number doesn't exhibit a pattern of repetition; instead, the different digits succeed in a seemingly random fashion. The following chart compares the first few digits of the decimal and duodecimal representation of several of the most important algebraic and transcendental irrational numbers. Some of these numbers may be perceived as having fortuitous patterns, making them easier to memorize, when represented in one base or the other.
Algebraic irrational number  In decimal  In duodecimal / dozenal 
√2 (the length of the diagonal of a unit square)  1.41421356237309... (≈ 1.414)  1.4B79170A07B857... (≈ 1.5) 
√3 (the length of the diagonal of a unit cube, or twice the height of an equilateral triangle of unit side)  1.73205080756887... (≈ 1.732)  1.894B97BB968704... (≈ 1.895) 
√5 (the length of the diagonal of a 1×2 rectangle)  2.2360679774997... (≈ 2.236)  2.29BB132540589... (≈ 2.2A) 
φ (phi, the golden ratio = ^{(1+√5)}⁄_{2})  1.6180339887498... (≈ 1.618)  1.74BB6772802A4... (≈ 1.75) 
Transcendental irrational number  In decimal  In duodecimal / dozenal 
π (pi, the ratio of circumference to diameter)  3.1415926535897932384626433 8327950288419716939937510... (≈ 3.1416) 
3.184809493B918664573A6211B B151551A05729290A7809A492... (≈ 3.1848) 
e (the base of the natural logarithm)  2.718281828459045... (≈ 2.718)  2.8752360698219B8... (≈ 2.875) 
The first few digits of the decimal and dozenal representation of another important number, the EulerMascheroni constant (the status of which as a rational or irrational number is not yet known), are:
Number  In decimal  In duodecimal / dozenal 
γ (the limiting difference between the harmonic series and the natural logarithm)  0.57721566490153... (~ 0.577)  0.6B15188A6760B3... (~ 0.7) 
The case for the duodecimal system was put forth at length in F. Emerson Andrews' 1935 book New Numbers: How Acceptance of a Duodecimal Base Would Simplify Mathematics. Emerson noted that, due to the prevalence of factors of twelve in many traditional units of weight and measure, many of the computational advantages claimed for the metric system could be realized either by the adoption of tenbased weights and measure or by the adoption of the duodecimal number system.
Rather than the symbols 'A' for ten and 'B' for eleven as used in hexadecimal notation and vigesimal notation (or 'T' and 'E' for ten and eleven), he suggested in his book and used a script X and a script E, (U+1D4B3) and (U+2130), to represent the digits ten and eleven respectively, because, at least on a page of Roman script, these characters were distinct from any existing letters or numerals, yet were readily available in printers' fonts. He chose for its resemblance to the Roman numeral X, and as the first letter of the word "eleven".
Another popular notation, introduced by Sir Isaac Pitman, is to use a rotated 2 to represent ten and a rotated or horizontally flipped 3 (which again resembles ) to represent eleven. This is the convention commonly employed by the Dozenal Society of Great Britain and has the advantage of being easily recognizable as digits because of their resemblance in shape to existing digits. On the other hand, the Dozenal Society of America adopted for some years the convention of using an asterisk * for ten and a hash # for eleven. The reason was the symbol * resembles a struckthrough X while # resembles a doublystruckthrough 11, and both symbols are already present in telephone dials. However, critics pointed out these symbols do not look anything like digits. Some other systems write 10 as ɸ (a combination of 1 and 0) and eleven as a cross of two lines (+, x, or † for example). Problems with these symbols are evident, most notably that most of them do not fit on most calculator displays ( being an exception, although "E" is used on calculators to indicate an error message). However, 10 and 11 do fit, both within a single digit (11 fits as is, while the 10 has to be tilted sideways, resulting in a character that resembles an O with a macron, ō or 0). A and B also fit (although B must be represented as lowercase "b" and as such, 6 must have a bar over it to distinguish the two figures) and are used on calculators for bases higher than ten.
In 'Little Twelvetoes', American television series Schoolhouse Rock! portrayed an alien child using basetwelve arithmetic, using 'dek', 'el', and 'doh' as names for ten, eleven, and twelve, and Andrews' scriptX and scriptE for the digit symbols. ("Dek" is from the prefix "deca," "el" being short for "eleven" and "doh" an apparent shortening of "dozen.")
The Dozenal Society of America and the Dozenal Society of Great Britain promote widespread adoption of the basetwelve system. They use the word dozenal instead of "duodecimal" because the latter comes from Latin roots that express twelve in baseten terminology.
The renowned mathematician and mental calculator Alexander Craig Aitken was an outspoken advocate of the advantages and superiority of duodecimal over decimal:
“  The duodecimal tables are easy to master, easier than the decimal ones; and in elementary teaching they would be so much more interesting, since young children would find more fascinating things to do with twelve rods or blocks than with ten. Anyone having these tables at command will do these calculations more than oneandahalf times as fast in the duodecimal scale as in the decimal. This is my experience; I am certain that even more so it would be the experience of others.  ” 
— A. C. Aitken, in The Listener, January 25th, 1962^{[3]}

“  But the final quantitative advantage, in my own experience, is this: in varied and extensive calculations of an ordinary and not unduly complicated kind, carried out over many years, I come to the conclusion that the efficiency of the decimal system might be rated at about 65 or less, if we assign 100 to the duodecimal.  ” 
— A. C. Aitken, The Case Against Decimalisation (Edinburgh / London: Oliver & Boyd, 1962)^{[4]}

In Leo Frankowski's Conrad Stargard novels, Conrad introduces a duodecimal system of arithmetic at the suggestion of a merchant, who is accustomed to buying and selling goods in dozens and grosses, rather than tens or hundreds. He then invents an entire system of weights and measures in base twelve, including a clock with twelve hours in a day (rather than twentyfour.)
