The poinsettia was basically designed while passenger in a car on our way to a Xmas lunch in Jutland, 3 hours driving. The flower takes some time to fold, but is worth it, and offers a lot of creative variations.
Use thin, red paper with a greenish or brownish back. Kraft wrapping paper will be excellent.
See also weekly fold 2015-02.
This method provides exactly the creases we need. Otherwise use a template.
1. Square paper. 20x20 cm is good, 15x15 is usable. You also need scissors and a stick.
3. We vill mark the center of one of the squares. Diagonal fold, mark only the center.
5. Mark center of other diagonal.
7. Fold the opposite, closed corner to the center mark.
8. Fold back, aligning with the edge.
9. Fold the other closed corner up along the previous fold.
11. Now you have ten layers, two and two forming a segment of the pentagon.
12. Cut along the innermost edge.
16. Adjust all corner lines in and mid lines out.
18. Fold a flap up vertically.
20. Press the top flat...
21. ...and 2/3 of the sides.
22. Fold the side in from the open end, until the lines meet.
24. Continue diagonally to the center and press flat.
25. Fold the triangle up towards the open ends.
26. Repeat with all five sides. This is the lily base for a pentagon.
27. Mark the triangle tip down to the mid line.
29. Side corner to the center, mark only from the mid line and up.
31. Repeat in the other side.
Sink to make the flower center
33. Fold the bottom corner to the triangle tip.
34. Use a tool to make a sharp crease.
36. Note that the crease matches the triangle tip. With other polygons (e.g. squares) this is the mark to use for the previous fold.
37. Repeat the fold the other way, to make it neutral. We will make a sink fold.
39. Begin to fold down in the sink line...
41. ...until the the center is all down. Keep the now reversed folds sharp.
42. Press flat. Seen from the bottom.
44. Pull out two neighbor leaves.
45. Flat between the mid corners.
46. Use the preliminary folds to shape a small up-triangle...
48. ...keep the leaf layers on the outside...
49. ...and assemble flat.
50. Close together again.
51. Lay flat with the re-arranged side up.
52. Make a crease from the corner to the bottom of the new pocket.
54. Repeat in the other end.
55. Enforce the fold by closing...
57. ...and flatten the V.
58. Fold the corner to the middle, along the crease.
62. Repeat with all five leaf intersections.
63. End with closed corners and a leaf up.
64. Fold in the corner. From the bottom as far as it goes, from the top so that it matches the mark of the preliminary crease.
65. Repeat in the other side...
66. ...and with all five leaves.
Opening the flower
68. Pull out the leaves carefully.
69. Check that the corners are freed.
70. All five leaves pulled out.
71. Curl the leaves over a hard edge, down where the meet.
72. Seen from the bottom.
73. Thus the leaf almost folds there.
74. Repeat with all five leaves.
75. Seen from the top. A nice flower, but we will make another center.
76. Fold all leaves downwards (seen from below).
77. Seen from above. The center tends to crumble.
78. Make sure the folds lie nicely.
80. Fold the ribs in half vertically.
81. Pairwise towards eachother, at each leaf.
84. Repeat for all five leaves.
85. Press the center together and down into the flower.
87. Right now the flower is attacked by a crumbling virus.
90. Adjust the leaf corners.