It's the Great Icosihedron

Please let me know if there are any errors in the color table.

The Great Icosihedron is the most complex of the non-convex (Kepler-Poinsot) regular polyhedra.  It is composed of 20 intersecting equilateral triangles.  The visible surface of a model consists of 120 long isoscelese triangles and 60 short isoscelese triangles.  A model can be built from 12 units containing 10 long triangles and 5 short triangles.


First cut out all the parts of the visible surface, leaving tabs along all edges.  Then, using a color table or color map, mark the non-visible side of each part with its location on the color map or table and the location of the adjacent part along each edge.

Apply glue to the tabs on each side of an edge and press the tabs together.  When a unit is completed, set it aside until the glue dries. A unit will resemble a non-convex pyramid with a brim like a party hat.

When all 12 units have been built, glue the small triangles together according to the color map.  Make sure each facial plane is as flat as possible, contains 9 triangles (6 long ones and 3 short ones) of the same color. and that pairs of facial planes are parallel.

The models use these colors (the capital letter is used in the table):

	Blue		Pink
	Cyan		Red
	Green		Violet
	light greeN		White
	Orange		Yellow

The color table for a 5 color model is (where A-Z means the short triangle of color A borders the short triangle of color Z indicated in the second line of the table entry)

  +---------------------------------------------------------------+
 +                 long triangles            +  short triangles  +
 |   | a | b | c | d | e | f | g | h | i | j | k | l | m | n | o |
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 1 | R | B | G | R | O | G | Y | O | B | Y |B-Y|R-O|G-Y|O-G|Y-O|
 |   |   |   |   |   |   |   |   |   |   |   |2'k| 4k| 3k|5'k|6'k|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 2 | G | Y | R | G | O | R | B | O | Y | B |Y-B|G-Y|R-G|O-Y|B-G|
 |   |   |   |   |   |   |   |   |   |   |   |1'k|6'l|3'n| 5m| 4o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 3 | R | Y | G | R | B | G | O | B | Y | 0 |Y-G|R-B|G-R|B-G|O-B|
 |   |   |   |   |   |   |   |   |   |   |   | 1m| 5l|2'n|6'm|4'o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 4 | B | O | R | B | Y | R | G | Y | O | G |O-R|B-O|R-B|Y-R|G-B|
 |   |   |   |   |   |   |   |   |   |   |   | 1l|3'l|6'n|5'm| 2o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 5 | B | G | Y | B | R | Y | O | R | G | O |G-O|B-R|Y-O|R-Y|O-R|
 |   |   |   |   |   |   |   |   |   |   |   |1'l| 3l| 2n|4'm|6'o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 6 | R | O | B | R | G | B | Y | G | O | Y |O-Y|R-O|B-R|G-B|Y-G|
 |   |   |   |   |   |   |   |   |   |   |   |1'l|5'l|4'n|3'm|2'o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |6' | O | R | Y | O | G | Y | B | G | R | B |O-Y|Y-G|G-B|B-R|R-O|
 |   |   |   |   |   |   |   |   |   |   |   | 1o| 2l| 3n| 4m| 5o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |5' | G | B | O | G | R | O | Y | R | B | C |G-O|O-R|R-Y|Y-O|B-R|
 |   |   |   |   |   |   |   |   |   |   |   | 1n| 6l| 4n|2'm|3'o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |4' | O | B | G | O | Y | G | R | Y | B | Y |O-R|G-B|Y-R|R-B|B-O|
 |   |   |   |   |   |   |   |   |   |   |   |1'o|2'l| 5n| 6m| 3o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |3' | Y | R | O | Y | B | O | G | B | R | G |Y-G|O-B|B-G|G-R|R-B|
 |   |   |   |   |   |   |   |   |   |   |   |1'n| 4l| 6n| 2m|5'o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |2' | Y | G | B | Y | O | B | R | O | G | R |Y-B|B-G|O-Y|R-G|G-Y|
 |   |   |   |   |   |   |   |   |   |   |   | 1k|4'l|5'n| 3m| 6o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |1' | B | R | Y | B | O | Y | G | O | R | G |B-Y|Y-O|O-G|G-Y|R-O|
 |   |   |   |   |   |   |   |   |   |   |   | 2k| 6k| 5k|3'k|4'k|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |   | a | b | c | d | e | f | g | h | i | j | k | l | m | n | o |
 +                 long triangles            +  short triangles  +
 +---------------------------------------------------------------+
A color map of the 5 color model can be found at
https://paulscottinfo.ipage.com/polyhedra/kepler-poinsot/great-icosah/gr-icosah-construct-analysi.gif.

The color table for a 10 color model is
 +---------------------------------------------------------------+
 +                 long triangles            +  short triangles  +
 |   | a | b | c | d | e | f | g | h | i | j | k | l | m | n | o |
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 1 | V | R | B | V | P | B | Y | P | R | Y |W-P|N-Y|O-R|C-V|G-B|
 |   |   |   |   |   |   |   |   |   |   |   | 2l| 3m| 4o| 5l| 6m|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 2 | G | Y | N | G | B | N | W | B | Y | W |R-B|P-W|V-Y|C-G|O-N|
 |   |   |   |   |   |   |   |   |   |   |   | 3n| 1k| 6l|4'k|5'o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 3 | R | N | W | R | O | W | P | O | N | P |C-O|V-P|Y-N|B-R|G-W|
 |   |   |   |   |   |   |   |   |   |   |   |6'n| 4k| 1l| 2k|5'n|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 4 | Y | C | O | Y | V | O | N | V | C | N |P-V|W-N|G-C|B-Y|R-O|
 |   |   |   |   |   |   |   |   |   |   |   | 3l|6'm|2'o| 5m| 1m|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 5 | O | B | G | O | R | G | C | R | B | C |P-R|V-C|Y-B|N-O|W-G|
 |   |   |   |   |   |   |   |   |   |   |   | 6n| 1n| 4n|2'n|3'n|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 | 6 | P | G | C | P | W | C | V | W | G | V |N-W|Y-V|B-G|R-P|O-C|
 |   |   |   |   |   |   |   |   |   |   |   |4'l| 2m| 1o| 5k|3'm|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |6' | C | W | P | C | G | P | V | G | W | V |B-G|Y-V|N-W|O-C|R-P|
 |   |   |   |   |   |   |   |   |   |   |   |1'n|2'k| 4l| 3k|5'm|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |5' | G | R | O | G | B | O | C | B | R | C |Y-B|V-C|P-R|W-G|N-O|
 |   |   |   |   |   |   |   |   |   |   |   |4'o|1'o|6'o| 3o| 2o|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |4' | O | V | Y | O | C | Y | N | C | V | N |G-C|W-N|P-V|R-O|B-Y|
 |   |   |   |   |   |   |   |   |   |   |   | 2n| 6k|3'l|1'k|5'k|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |3' | W | O | R | W | N | R | P | N | O | P |Y-N|V-P|C-O|G-W|B-R|
 |   |   |   |   |   |   |   |   |   |   |   |1'l|4'm| 6o| 5o|2'm|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |2' | N | B | G | N | Y | G | W | Y | B | W |V-Y|P-W|R-B|O-N|C-G|
 |   |   |   |   |   |   |   |   |   |   |   |6'l|1'm|3'o| 5n| 4m|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |1' | B | P | V | B | R | V | Y | R | P | Y |O-R|N-Y|W-P|G-B|C-V|
 |   |   |   |   |   |   |   |   |   |   |   |4'n|3'k|2'l|6'k|5'l|
 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
 |   | a | b | c | d | e | f | g | h | i | j | k | l | m | n | o |
 +                 long triangles            +  short triangles  +
 +---------------------------------------------------------------+
A 10 color map can be found in  http://www.korthalsaltes.com/pdf/collection_004.PDF
under Great Icosahedron, in 10 colors, Small Version.