TO make, by folding and cutting, an equilateral triangle, a hexagon, a three-pointed star, a six-pointed star, a trefoil, a hexafoil, a three-leaved rosette, and a six-leaved rosette, from a square, a circle, or any regular or irregular plane figure.

The Square

The Square 75

Fig. \

The Square 76The Square 77

FIg-3

The Square 78The Square 79

Fig. 5

Beginning with the square, Fig. 1, fold I on 2, folding from o, and crease with the thumb-nail, thus obtaining Fig. 2.

To obtain Fig. 3, trisect the 180°fold in Fig. 2, and fold the right part on the adjoining one, folding from o. For Fig. 4, fold the remaining part, seen in Fig. 3, on top of the first fold, and crease. For Fig. 5, bisect and fold Fig. 4.

The Square 80

The Equilateral Triangle

Fold to Fig. 4, and cut from 1 to 2. The line 1-2 must be at right angles to 3-0-.

The Equilateral Triangle 81

The Regular Hexagon

Fold to Fig. 4, and cut from 1 to 2. Points 1 and 2 must be equally distant from o.

The Regular Hexagon 82

The Three-Pointed Star

Fold to Fig. 4, and cut from 1 to 2. Point 2 is obtained by quadrisecting 3-0.

The Six-Pointed Star

Fold to Fig. 5, and cut from 1 to 2. Point 2 is obtained by trisecting 3-0.

The Six Pointed Star 83

The Trefoil

Fold to Fig. 4, and cut from 1 to 2. Point 2 is the intersection of the line 3-0 and the arc. The arc should be a semicircle, having its centre on the line 1-0.

The Trefoil 84

The Trefoil

Fold to Fig. 4, and cut from 1 to 2. The arc 4-1 should be a quadrant, with 3 as centre. The line 2-4-1 must be at right angles with 5-0.

The Trefoil 85The Trefoil 86

The Hexafoil

Fold to Fig. 5, and cut from 1 to 2. Point 2 is the tangential union of the arc and the line 3-0. The arc should be a semicircle, having its centre on the line 1-0.

The Hexafoil 87

The Hexafoil

Fold to Fig. 5, and cut from 1 to 2. The line 2-4 must be at right angles to 1-0, and the arc 3-1 should be a quadrant with 4 as centre.

Three-Leaved Rosettes

Fold to Fig. 3, and cut from 1 to 2.

Three Leaved Rosettes 88Three Leaved Rosettes 89Three Leaved Rosettes 90Three Leaved Rosettes 91

The Circle

The Circle 92

FiG I

The Circle 93

Tig 2

The Circle 94The Circle 95The Circle 96

For the triangle, fold to Fig. 3, and cut from 1 to 2. For the hexagon, fold to Fig. 4, and cut from 1 to 2. For the six-pointed star, fold to Fig 5, and cut from 1 to 2. Point 2 is obtained by trisecting 3-0.

The Circle 97

SIX-LEAVED ROSETTES

Fold to Fig. 5, and cut from 1 to 2.

SIX LEAVED ROSETTES 98SIX LEAVED ROSETTES 99SIX LEAVED ROSETTES 100SIX LEAVED ROSETTES 101