heptagon Challenge

Challenge yourself to create a polyhedron with three or more regular heptagon (7 sided) faces. Jump to success with the pattern below. This one has 24 faces total; with four regular heptagon faces, eight trapezoid faces, four diamond faces, and eight triangle faces.

Step 2

Make the Base.  Cut out Base Part 1 and Part 2 by cutting on all black lines, including the black line between the two Flap A’s and between the two Flap B’s.  Fold all green lines as valley folds.

STEP 3

Continue to assemble Base.  On both Base Part 1 and Part 2, glue Flap A to the other Flap A, Flap B to the other Flap B, Flap C to the other Flap C, Flap D to the other Flap D, Flap E to the other Flap E, and Flap F to the other Flap F.

Step 4

Complete the Base by connecting Base Parts 1 and 2.  Start  by gluing Flaps M, N,  and O on Part 1 to Flaps M, N, and O on Part 2.  Next glue the two Flaps L’s on Part 1 to the two Flap L’s on Part 2, and the two Flap W’s on Part 1 to the two Flap W’s on Part 2.  Then glue Flaps H, G, and J on Part 1 to Flaps H, G, and J and on Part 2.  Next glue Flaps V, U, and T on Part 1 to Flaps V, U, and T on Part 2. Then glue the two Flaps K’s on Part 1 to the two Flap K’s on Part 2, and the two Flap S’s on Part 1 to the two Flap S’s on Part 2.  Finally glue Flaps R, Q, and P on Part 1 to Flaps R, Q, and P on Part 2.   You now have a 24-sided polyhedron (icositetrahedron) with four regular heptagon faces.  Continue if you want to stellate (add points to) your polyhedron. 

Step 5

Make the points.  Cut out the 24 points by cutting on all black lines.  Fold green lines as valley folds on each part.

Step 6

Complete the 24 points by gluing Flap A to the other Flap A on each point.

Step 7

Connect the points to the base using the glue flaps on the points.  Four Point Type 1’s to the heptagon faces.  Four Point Type 2’s to the diamond faces.  Eight Point Type 3’s to the triangle faces.  Four Point Type 4’s to the large trapezoid faces.  And four Point Type 5’s to the small trapezoid faces.