Polygrammagick

Magic squares, in which each row, column, and diagonal of a square of numbers add up to the same total, are well-known and have been for thousands of years; magic polygrams (also known as magic stars), in which rows of interconnected numbers do the same, are far less so.
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As with magic squares, there are many different magic arrangements for any given total above 26 (the hexagram), but you can see a representative polygram for the totals 26-82 (6-20 sides) by pressing Next or Prev above (or here).

Some Bigger Magic Stars

stars.zip (Stars 6-49)

stars1.zip (Stars 50-69)

stars2.zip (Stars 70-100, 166)

Zipped text files of stars with from 6 to 100 vertices, plus the 166-agram (see below). They were found using Pascal and C.

Numerologists will be especially interested in this magic polygram:

Data for a 166-v magic polygram (Constant=666) (found 23/ix/2003).

(332,331,  1,  2),(  6,  1,330,329),(  2,330, 23,311),
(329, 23,310,  4),(311,310, 42,  3),(  4, 42,328,292),
(  3,328,327,  8),(292,327, 40,  7),(  8, 40,325,293),
(  7,325,324, 10),(293,324, 44,  5),( 10, 44,326,286),
(  5,326,323, 12),(286,323, 48,  9),( 12, 48,322,284),
(  9,322,321, 14),(284,321, 50, 11),( 14, 50,320,282),
( 11,320,319, 16),(282,319, 52, 13),( 16, 52,318,280),
( 13,318,317, 18),(280,317, 54, 15),( 18, 54,316,278),
( 15,316,315, 20),(278,315, 56, 17),( 20, 56,314,276),
( 17,314,313, 22),(276,313, 58, 19),( 22, 58,312,274),
( 19,312,309, 26),(274,309, 62, 21),( 26, 62,308,270),
( 21,308,307, 30),(270,307, 65, 24),( 30, 65,306,265),
( 24,306,305, 31),(265,305, 71, 25),( 31, 71,304,260),
( 25,304,303, 34),(260,303, 76, 27),( 34, 76,302,254),
( 27,302,301, 36),(254,301, 83, 28),( 36, 83,300,247),
( 28,300,299, 39),(247,299, 91, 29),( 39, 91,298,238),
( 29,298,296, 43),(238,296,100, 32),( 43,100,297,226),
( 32,297,291, 46),(226,291,116, 33),( 46,116,295,209),
( 33,295,289, 49),(209,289,133, 35),( 49,133,294,190),
( 35,294,290, 47),(190,290,149, 37),( 47,149,288,182),
( 37,288,281, 60),(182,281,165, 38),( 60,165,287,154),
( 38,287,277, 64),(154,277,194, 41),( 64,194,285,123),
( 41,285,283, 57),(123,283,215, 45),( 57,215,279,115),
( 45,279,275, 67),(115,275,225, 51),( 67,225,273,101),
( 51,273,272, 70),(101,272,240, 53),( 70,240,271, 85),
( 53,271,269, 73),( 85,269,257, 55),( 73,257,268, 68),
( 55,268,266, 77),( 68,266,263, 69),( 77,263,267, 59),
( 69,267,264, 66),( 59,264,262, 81),( 66,262,259, 79),
( 81,259,252, 74),( 79,252,255, 80),( 74,255,253, 84),
( 80,253,261, 72),( 84,261,258, 63),( 72,258,250, 86),
( 63,250,256, 97),( 86,256,249, 75),( 97,249,242, 78),
( 75,242,251, 98),( 78,251,248, 89),( 98,248,233, 87),
( 89,233,245, 99),( 87,245,246, 88),( 99,246,239, 82),
( 88,239,244, 95),( 82,244,237,103),( 95,237,241, 93),
(103,241,232, 90),( 93,232,236,105),( 90,236,234,106),
(105,234,235, 92),(106,235,231, 94),( 92,231,230,113),
( 94,230,228,114),(113,228,229, 96),(114,229,221,102),
( 96,221,227,122),(102,227,220,117),(122,220,217,107),
(117,217,224,108),(107,224,223,112),(108,223,216,119),
(112,216,218,120),(119,218,219,110),(120,219,206,121),
(110,206,222,128),(121,222,214,109),(128,214,213,111),
(109,213,212,132),(111,212,208,135),(132,208,202,124),
(135,202,211,118),(124,211,205,126),(118,205,207,136),
(126,207,204,129),(136,204,201,125),(129,201,199,137),
(125,199,203,139),(137,203,196,130),(139,196,200,131),
(130,200,198,138),(131,198,210,127),(138,210,184,134),
(127,184,197,158),(134,197,195,140),(158,195,172,141),
(140,172,193,161),(141,193,189,143),(161,189,174,142),
(143,174,192,157),(142,192,188,144),(157,188,176,145),
(144,176,191,155),(145,191,183,147),(155,183,180,148),
(147,180,187,152),(148,187,181,150),(152,181,167,166),
(150,167,170,179),(166,170,168,162),(179,168,173,146),
(162,173,178,153),(146,178,186,156),(153,186,164,163),
(156,164,175,171),(163,175,151,177),(171,151,185,159),
(177,185,243, 61),(159,243,104,160),( 61,104,169,332),
(160,169,331,  6).

Outer numbers=
332,  6,  2,329,311,  4,  3,292,  8,  7,
293, 10,  5,286, 12,  9,284, 14, 11,282,
 16, 13,280, 18, 15,278, 20, 17,276, 22,
 19,274, 26, 21,270, 30, 24,265, 31, 25,
260, 34, 27,254, 36, 28,247, 39, 29,238,
 43, 32,226, 46, 33,209, 49, 35,190, 47,
 37,182, 60, 38,154, 64, 41,123, 57, 45,
115, 67, 51,101, 70, 53, 85, 73, 55, 68,
 77, 69, 59, 66, 81, 79, 74, 80, 84, 72,
 63, 86, 97, 75, 78, 98, 89, 87, 99, 88,
 82, 95,103, 93, 90,105,106, 92, 94,113,
114, 96,102,122,117,107,108,112,119,120,
110,121,128,109,111,132,135,124,118,126,
136,129,125,137,139,130,131,138,127,134,
158,140,141,161,143,142,157,144,145,155,
147,148,152,150,166,179,162,146,153,156,
163,171,177,159, 61,160.

Inner numbers=
331,  1,330, 23,310, 42,328,327, 40,325,
324, 44,326,323, 48,322,321, 50,320,319,
 52,318,317, 54,316,315, 56,314,313, 58,
312,309, 62,308,307, 65,306,305, 71,304,
303, 76,302,301, 83,300,299, 91,298,296,
100,297,291,116,295,289,133,294,290,149,
288,281,165,287,277,194,285,283,215,279,
275,225,273,272,240,271,269,257,268,266,
263,267,264,262,259,252,255,253,261,258,
250,256,249,242,251,248,233,245,246,239,
244,237,241,232,236,234,235,231,230,228,
229,221,227,220,217,224,223,216,218,219,
206,222,214,213,212,208,202,211,205,207,
204,201,199,203,196,200,198,210,184,197,
195,172,193,189,174,192,188,176,191,183,
180,187,181,167,170,168,173,178,186,164,
175,151,185,243,104,169.

If you'd like to know much more about magic polygrams, such as why there is no pure magic pentagram, please visit this site maintained by an expert hobbyist:

Harvey Heinz's Magic Stars

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