Regular Octagon
Regular Octagon
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Regular Octagon |
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Folding sheets Regular Octagon Welcome page Back to the list |
Aveuglami project - folding sheet
Regular Octagon
| Author | Diverse |
| Category | orimaths |
| Difficulty | * |
| Format | square |
| Base | - |
| Text | A regular octagon is a regular polygon with 8 sides. Two construction methods are described below.
a - Method 1 - square sheet We use the beginning of a base of the frog. First instar of a frog base 1. Start with the preliminary base, oriented free ends downwards. To facilitate the formation of the petal folds from step 16 to step 20, it is recommended to start by making a blintz base, then completely unfold the result to make a preliminary base. The additional oblique folds are not involved in the creation of the preliminary base. This passage through a blintz base is of no use if we are only interested in the first stage of the base of the frog. 2. Form a valley fold by bringing the upper right edge of the right front flap over the vertical middle fold. Unfold. Fold over the same fold in the other direction. Unfold. 3. Raise the right part of the front flap vertically. Slide a finger inside the triangular pocket to open it. Flatten it using the folds made in the previous step. The flattened flap transforms into a front triangle to which are connected, by two hinged edges, two small triangles (one left and one right) of which part is hidden and part is visible below the lower edge of the front triangle. The whole forms a symmetrical quadrilateral in relation to a vertical median axis, with a long sharp point upwards and a short point downwards. 4. Flip the fold from left to right. 5. Form a valley fold by bringing the upper right edge of the right front flap over the vertical middle fold. Unfold. 6. Raise the right part of the front flap vertically. Slide a finger inside the triangular pocket to open it. Flatten it using the folds made in the previous step. 7. Rotate the small left front flap from left to right along the center vertical axis. 8. Rotate the left front flap from left to right along the center vertical axis. 9. Form a valley fold by bringing the upper right edge of the right front flap over the vertical middle fold. Unfold. 10. Raise the right part of the front flap vertically. Slide a finger inside the triangular pocket to open it. Flatten it using the folds made in the previous step. 11. Flip the fold from right to left. 12. Rotate the small left front flap from left to right along the center vertical axis. 13. Rotate the left front flap from left to right along the center vertical axis. 14. Form a valley fold by bringing the upper right edge of the right front flap over the vertical middle fold. Unfold. 15. Raise the right part of the front flap vertically. Slide a finger inside the triangular pocket to open it. Flatten it using the folds made in the previous step step 14. We obtain a diamond shape with a closed point elongated upwards and a shorter point formed by 4 small free points distributed 2 by 2 around the vertical axis. The small points are delimited by the top of the triangle of the closed point. 16. Fold each small tip along the top edge of the closed tip triangle. Mark firmly. Unfold. 17. Open the fold so that the center is hollow. From each vertex of the square leaves a valley fold joining the center. When we start from a summit going towards the center, we encounter a mixed fold (part in valley, part in mountain) perpendicular to the fold that we follow. 18. Fold each corner of the square towards the center, relying on the mixed fold perpendicular to the valley fold which joins the vertex to the center. Mark the fold well. The result is a regular octagonal shape with one smooth side. b - Method 2 with a template We use an A4 size sheet. This method involves cutting a rectangular strip which will serve as a measure to make the octagon. b1 - Prepare a square. 1. Take an A4 sheet of paper, hold it vertically. 2. Bring, by a valley fold at 45° from left to right and from top to bottom, the upper edge along the right edge. We obtain a right-angled trapezoid with one point pointing upwards. This point carries a triangular flap, the lower horizontal edge of which delimits the top of a rectangle of simple thickness. 3. Fold and unfold the lower rectangle several times in the valley and in the mountains, leaning on the lower edge of the triangular flap. Mark the fold well. 4. Cut out the bottom rectangular strip and set it aside. 5. Open the triangular tip so that the diagonal fold is in a valley. We obtain a square shape with a diagonal marked in a valley. 6. Rotate the fold so that the marked diagonal goes from the lower left corner to the upper right corner. 7. Bring, using a valley fold from left to right, the upper left corner to the lower right corner. Unfold b2 - Prepare the rectangular strip. 8. Take the rectangular strip obtained in step b2-4 and hold it in a horizontal position. 9. Bring, using a valley fold from top to bottom, the upper edge to the lower edge. Mark the fold well. We obtain a rectangular shape of double thickness. b3 - Build the octagon. 10. Hold the folded square sheet along one of the diagonals. We have a triangular shape composed of two flaps articulated by a hinge fold carried by a diagonal of the original square. 11. Slide the rectangular strip inside the triangular shape so that it rests, at its greatest length, on the bottom of the triangular shape. The rectangular shape will probably stick out to one side or the other of the triangular shape. 12. Slide the rectangular shape inside the triangular shape, while holding it on the bottom, so that it no longer protrudes. 13. Rotate the fold until the hinge fold is horizontal, open tip facing up. 14. Starting from the left tip attached to the hinge fold and going to the right, detect the extra thickness corresponding to the start of the hidden rectangular strip. We can help ourselves by slightly opening the triangle to find the start of the strip. 15. Fold the left tip into a valley, from left to right, along the left edge of the hidden rectangular shape. Mark the fold well. Unfold. 16. Starting from the right tip attached to the hinge fold and going towards the left, detect the extra thickness corresponding to the start of the hidden rectangular strip. We can help ourselves by slightly opening the triangle to find the start of the strip. 17. Fold the left tip into a valley, from right to left, along the right edge of the hidden rectangular shape. Mark the fold well. Unfold 18. Open the fold from top to bottom around the hinge fold. The left and right corners of the square each have a vertical fold, divided in half into a valley fold and a mountain fold. 19. Fold, using a valley fold from left to right, the left corner using the vertical fold located to its right. You have to reverse the part of the fold that is in the mountains. 20. Fold, using a valley fold from right to left, the right corner using the vertical fold located to its left. You have to reverse the part of the fold that is in the mountains. 21. Fold the square sheet along the diagonal that was not used. We have a quadrilateral composed of two parts articulated by a hinge fold carried by a diagonal of the original square. 22. Slide the rectangular strip inside the quadrilateral so that it rests, along its greatest length, on the bottom of the shape. The rectangular shape will probably stick out on one side or the other of the quadrilateral. 23. Slide the rectangular shape inside the quadrilateral, while keeping it on the bottom, so that it no longer protrudes. 24. Rotate the fold until the hinge fold is horizontal, with the open side facing up. 25. Starting from the left point attached to the hinge fold and going towards the right, detect the extra thickness corresponding to the start of the hidden rectangular strip. We can help ourselves by slightly opening the triangle to find the start of the strip. 26. Fold the left tip into a valley, from left to right, along the left edge of the hidden rectangular shape. Mark the fold well. Unfold. 27. Starting from the right tip attached to the hinge fold and going towards the left, detect the extra thickness corresponding to the start of the hidden rectangular strip. We can help ourselves by slightly opening the quadrilateral to find the start of the strip. 28. Fold the left tip into a valley, from right to left, along the right edge of the hidden rectangular shape. Mark the fold well. Unfold. 29. Open the fold from top to bottom around the hinge fold. The left and right corners of the square each have a vertical fold, divided in half into a valley fold and a mountain fold. 30. Fold, using a valley fold from left to right, the left corner using the vertical fold located to its right. You have to reverse the part of the fold that is in mountain. 31. Fold, using a valley fold from right to left, the right corner using the vertical fold located to its left. You have to reverse the part of the fold that is in mountain. 32. Remove the rectangular strip. 33. Turn the fold from right to left so that you have a smooth side facing you. Here is a regular octagon constructed in an almost magical way. |
| Contents | File |
| Regular Octagon - PDF file | ML-Orimaths11Ang.pdf |