The Regular Hyperstar _{o}^{n}S^{s}_{m}(sum)  
The Hyperstar of dimension (n) can be defined with help of the n dimensional Hyperspere by placing a number of circles on the hypersphere, the intersecting points of these circles are the points of the star. The order of the star (m) is defined as the number of starpoint the step (s) is defined on a defining circle as the point that follows the previous, ie on a circle with s=1 one gets a polygon (or magon), with s=2 to m/2 the starlines intersect and the figure (per circle) shows a regular pointed star, (higher step numbers merely for a reflection of already defined figures. The stars suborder (o) is defined as the amount of numbers per line (not necessarily intersection points) (in case of even m (s = m/2) connects all points through the cicles center to the opposed point) The Hyperstar is "Regular" when all numbers (order, step and suborder) are the same on each circle The Magic sum partakes in the hyperstars notation since thus far contineous sequences are seldom and the actual sum is dependent on their use (trick is also to minimize that sum) 

The Irregular Hyperstar _{{o1,..,o?}}^{n}S^{{s1,..,s?}}_{{m1,..,m?}}  
Defined as is the regular hyperstar but allows varying step "s", order "m" and/or suborder "o" (currently loosely defined, but allows for ^{2}S^{{2,2,3}}_{6}) Depending on future development subclassification might be defined. 
ADWORKS 
The Magic Encyclopedia ™ notation  
Harvey Heinz: Normal Star: N^{s}_{m} ≡ _{4}^{2}S^{s}_{m} 

The Magic Encyclopedia ™ article 
The Magic Tetrahedron _{3}^{3}S^{1}_{3}  

_{3}^{3}S^{1}_{3}(15)  01 06 09 11 08 02 05 07 03 04 
_{3}^{3}S^{1}_{3}(21)  11 06 03 01 04 10 07 05 09 08 
triangle based pyramid star _{3}^{3}S^{1}_{8}  
_{3}^{3}S^{1}_{8}(27)  02 11 13 17 14 01 12 07 08 05 
06 05 11 17 16 01 10 13 04 07 
The Magic Square based pyramid _{3}^{3}S^{1}_{5}  

_{3}^{3}S^{1}_{5}(18)  01 15 02 08 07 14 09 12 06 05 03 11 04 
_{3}^{3}S^{1}_{5}(24)  08 09 07 01 02 10 15 12 03 04 06 13 05 
_{3}^{3}S^{1}_{5}(24)  08 07 09 15 14 06 01 04 13 12 10 03 11 
_{3}^{3}S^{1}_{5}(30)  15 01 14 08 09 02 07 04 10 11 13 05 12 
square based pyramid star _{3}^{3}S^{1}_{10}  
_{3}^{3}S^{1}_{10}(36)  08 07 32 27 30 06 05 03 29 04 
08 07 16 19 14 06 05 11 13 12 

_{3}^{3}S^{1}_{10}(42)  15 14 38 26 36 13 12 03 35 04 
15 14 08 11 06 13 12 18 05 19 

_{3}^{3}S^{1}_{10}(66)  26 27 02 07 04 28 29 31 05 30 
26 27 18 15 20 28 29 23 21 22 

_{3}^{3}S^{1}_{10}(78)  25 26 02 14 04 27 28 37 05 36 
25 26 32 29 34 27 28 22 35 21 