## § Origami box pleating

• Box pleating: subdivide paper into grid, then create into grid.
• To creases into model, use the Elias stretch
• We get 3 types of creases: hinge, ridge, axial
• red for ridge, blue for hinge.
• hinge: what we cut along to dissect the model along hinges.
• ridge creases: creases that are diagonal / angle bisector of the polygons (in box pleating, is always square).
• BPstudio (box-pleating studio) is the tool used to make box pleating.

#### § Minimum grid size computatation

• (sum of lengths of tree edges * 2)/4.
• for an edge flap, it takes 2 * edgelen of perimeter when unfolded.
• for a river, it also takes 2 * riverlen of permiter when unfolded.
• in total, we take sum (2 * len) over all edges/rivers of perimeter.
• perimeter is 4 * square-side-len.
• So we get that square-side-len equals (sum of lengths of tree edges * 2)/.

#### § Axial box pleating

• In the folded model, pick an imaginary line on which only valley creases lie
• also, all the hinge creases are perpendicular to this imaginary line.
• A model is axial box pleated if there is an axis such that all hinge creases are orthogonal to this imaginary line.

#### § Axial plus i creases

• Only creases can be referred to as 'axial plus i'.
• The 'plus i' gives us how much higher we need to go.
• the ridges are the creases that allow go between 'axial plus i' to 'axial plus (i + 1)'.
• This gives us 3 types of creases: (1) hinges, which are orthogonal to the axis, (2) ridges, which connect 'axial plus i' creases, and the family of 'axial plus i' creases.
(Ridge)
(axial+1)---|--------/----------
|       /
(axial+0)---|------/-------------
(Hinge)
• If there is only one axis, then it is uni-axial.