Origami sheet - Cat with the Turned Head

Step 1.

Take a square sheet of paper, place it flat on the table, with the bottom edge horizontal.

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The corners of the square are at the top left, top right, bottom right, and bottom left.

Step 2.

Make a valley fold, vertical, bringing the right edge over to the left edge.

Crease well, then unfold.

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This just marks the vertical axis of symmetry.

Step 3.

Make a valley fold, vertical, bringing the right edge along the valley fold marking the vertical axis of symmetry.

Crease well, and leave it folded.

Step 4.

Make a valley fold, vertical, bringing the left edge along the valley fold marking the vertical axis of symmetry.

Carefully crease the fold, and let it fold.

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You get a vertical rectangle, consisting of two double-thickness rectangular flaps (one right and one left) connected by the vertical axis of symmetry.
On the front side, a slit follows the vertical axis.

Step 5.

Turn the folding from right to left.

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The folding is still a rectangle in a vertical position.
The vertical slit is on the table side.

Step 6.

Make a valley fold, horizontal, by bringing the bottom edge up to the top edge.

Carefully crease the fold, then unfold.

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You have just marked the horizontal axis of symmetry.
The horizontal axis is a valley (it forms a trough), and the vertical axis is a mountain (it forms a ridge).
The vertical slit is on the table side.

Step 7.

Make a 45° diagonal valley fold by bringing, from bottom to top towards the left, the right half of the bottom edge, along the vertical symmetry axis.

Crease the fold well, and leave it folded.

Step 8.

Make a 45° diagonal valley fold by bringing, from bottom to top towards the right, the left half of the bottom edge, along the vertical symmetry axis.

Crease the fold well, and leave it folded.

Step 9.

Turn the folding from right to left.

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The folding is a pentagon that has:
A horizontal top edge,
A vertical right edge,
A right oblique bottom edge,
A left oblique bottom edge,
A vertical left edge.
A vertical slit connects the middle of the horizontal top edge to the bottom point.

Step 10.

Form an oblique valley fold by bringing, from bottom to top towards the right, the lower left edge of the fold along the vertical axis of symmetry, making sure to let the underlying flap return without folding it.

Crease the fold well, and let it fold.

Step 11.

Form an oblique valley fold by bringing, from bottom to top towards the left, the lower right edge of the fold along the vertical axis of symmetry, making sure to let the underlying flap return without folding it.

Crease the fold well, and let it fold.

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The lower tip is covered at the front by two small right triangles side by side, which form a square in diamond position.

Step 12.

Unfold until you regain the rectangle in vertical position.

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Starting from the lower edge of the folding, in a clockwise direction we have:
The lower left point,
An oblique mountain fold,
An oblique valley fold,
A vertical slit,
An oblique valley fold,
An oblique mountain fold,
And the lower right point.

Step 13.

Transform the left oblique valley fold into a mountain fold, then turn this valley/mountain fold into an inside reverse fold.

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A double-layered triangular pocket has formed, partially covering the lower right part of the folding.
The opening of the pocket follows the right oblique mountain fold.

Step 14.

Fold this pocket against the left part of the folding, forming a valley fold along the vertical slit.

Turn the mountain fold of this small pocket into a valley fold, then turn this mountain/valley fold into an inside reverse fold.

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The small pocket now protrudes from the lower left part of the fold and seems to be caught between the front flap and the back flap.

Step 15.

Make an oblique valley fold by bringing the lower left edge of the small pocket from bottom to top to the right, onto the vertical symmetry axis.

Turn this valley fold into a mountain fold, then turn this valley/mountain fold into an inside reverse fold.

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On the front side, a quadruple-thickness point comes to cover the left part of the lower point of the fold.

Step 16.

We will now perform the manipulations on the lower right part of the fold:

Transform the right oblique valley fold into a mountain fold, then turn this valley/mountain fold into a reverse inside fold.

additional information

a double-thickness triangular pocket has formed, partially covering the lower left part of the fold.

Step 17.

Fold this pocket against the right part of the fold, forming a valley fold along the vertical slit. Transform the mountain fold of this small pocket into a valley fold, then turn this mountain/valley fold into a reverse inside fold.

additional information

the small pocket now protrudes from the lower right part of the fold and seems to be caught between the front flap and the back flap.

Step 18.

Form an oblique valley fold by bringing, from bottom to top to the left, the lower right edge of the small pocket to the vertical axis of symmetry.

Turn this valley fold into a mountain fold, then turn this valley/mountain fold into an inside reverse fold.

additional information

On the front side, a quadruple-thickness point comes to cover the right part of the lower point of the fold.
The fold is now a pentagon; on the front side, a vertical slit connects the middle of the upper horizontal edge to the lower point.
Two small free points come to cover the right and left parts of the lower point of the pentagon.
The horizontal axis of symmetry is a mountain.
The folding includes: a top left tip, a top right tip, a right tip, a lower back tip, two lower front tips, a left tip.

Step 19.

Form a horizontal valley fold, connecting the right and left tips of the folding.

Crease the fold well, then unfold.

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The folding now has two horizontal folds.
The horizontal axis of symmetry is a mountain fold, and a little higher, the horizontal valley fold.

Step 20.

Flip the lower part of the folding over the upper part, using the horizontal valley fold that was just created.

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The front flap is now triangular, and has a horizontal valley fold a little higher, relative to the bottom edge, which is a hinge edge.

Step 21.

Flip the upper part of the front flap over the lower part, using the horizontal valley fold. (Former horizontal axis of symmetry).

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The folding now consists of three flaps:
At the front, a lower flap in the shape of a triangle.
In the middle, a flap in the shape of a horizontal trapezoid.
At the back, an upper flap in a rectangular shape.

Step 22.

Form a valley fold by bringing the right edge of the rectangular flap from right to left onto the valley fold marking the vertical axis of symmetry.

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The fold should be marked only on the middle part of the edge. (Not at the ends)

Step 23.

Form a valley fold by bringing the left edge of the rectangular flap from left to right onto the valley fold marking the vertical axis of symmetry.

additional information

the fold should be marked only on the middle part of the edge. (Not at the ends)

Step 24.

Place the right thumb between the front flap and the middle flap.

Place the right index finger along the right slanted edge of the trapezoid.

Step 25.

Push down and to the left on the right index finger, to align the slanted edge of the trapezoid along the lower hinge edge. Flatten well the pocket that has formed.

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We have just created a pivot fold.

Step 26.

Place the left thumb between the front flap and the middle flap.

Place the left index finger along the left slanted edge of the trapezoid.

Step 27.

Push down and to the right on the left index finger, to align the slanted edge of the trapezoid along the lower hinge edge. Flatten well the pocket that has formed.

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A pivot fold has just been created.

Step 28.

Form an oblique valley fold by bringing, from bottom to top towards the right, the left vertical edge from the front lower right tip to horizontal.

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the small tip, initially facing 6 o'clock, is now facing 3 o'clock.

Step 29.

Transform the previous oblique valley fold into a mountain fold, then this valley/mountain fold into an inside reverse fold.

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the small tip, initially facing 6 o'clock, is now facing 3 o'clock.

Step 30.

Form an oblique valley fold by bringing the right vertical edge from the front lower left tip to horizontal.

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the small tip, initially facing 6 o'clock, is now facing 9 o'clock.

Step 31.

Transform the previous diagonal valley fold into a mountain fold, then turn this valley/mountain fold into an inside reverse fold.

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the small tip originally pointing at 6 o'clock is now pointing at 9 o'clock.

Step 32.

Close the folding by folding the left flap over the right flap, using the vertical axis of symmetry. (Existing valley fold).

Step 33.

Arrange the folding so that the hinge edge is the top edge, and the right part of the folding is a rectangle.

Step 34.

Make a diagonal valley fold along the diagonal connecting the bottom left corner and the top right corner of the rectangular right part of the front flap.

Carefully crease the fold, and let it stay folded.

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what was previously the lower right corner is now a double-layered triangular flap, whose free tip is oriented at 12 o'clock.

Step 35.

Turn the folding from right to left.

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the left part of the front flap is a rectangle.

Step 36.

Form an oblique valley fold along the diagonal connecting the lower right corner and the upper left corner of the rectangular left part of the front flap.

Mark the fold well, and let it fold.

additional information

what was previously the lower left corner is now a double-layered triangular flap, whose free tip is oriented at 12 o'clock.
We are going to form a rabbit ear with the triangular flap that was just mentioned.
The flap in question has a top edge, a right edge, and a hinge edge corresponding to the hypotenuse of the right triangle.

Step 37.

Fold down the free tip of the triangular flap to form a horizontal valley fold along the top hinge edge of the fold.

Crease the fold well, then unfold.

Step 38.

Form an oblique valley fold by bringing the right edge of the triangular flap along the hypotenuse.

Crease the fold well, then unfold.

Step 39.

Using the two previous valley folds, simultaneously bring the top edge and the right edge of the triangular flap onto the hypotenuse.

additional information

a small tip oriented toward the ceiling has formed. This is the rabbit ear.

Step 40.

Fold the rabbit ear to the left, against the fold.

Step 41.

Turn the fold from right to left.

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We are going to form a rabbit ear, using the triangular flap located on the right of the fold.
The flap in question has a top edge, a left edge, and a hinge edge corresponding to the hypotenuse of the right triangle.

Step 42.

Fold down the free tip of the triangular flap to form a horizontal valley fold along the top hinge edge of the fold.

Crease well, then unfold.

Step 43.

Form an oblique valley fold by bringing the left edge of the triangular flap along the hypotenuse.

Crease well, then unfold.

Step 44.

Using the two previous valley folds, simultaneously bring the top edge and the left edge of the triangular flap to the hypotenuse.

additional information

A small tip pointing toward the ceiling has formed. This is the rabbit ear.

Step 45.

Fold the rabbit ear to the right, against the fold.

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The fold has two large flaps (front and back) that are symmetrical, connected to each other by a top horizontal hinge edge.
On the ceiling side, a vertical line indicates a change in thickness of the large front flap.
The bottom right edge of this large front flap is a hinge edge, which connects this large flap to a tapered triangular flap, which itself has a small free tip corresponding to the rabbit ear.

Step 46.

Form a valley fold by bringing the bottom right edge of the front large flap along the vertical line marking the change in thickness.

Make sure to crease the fold well, then unfold.

Step 47.

Turn the folding from right to left.

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On the ceiling side, a vertical line marks a change in thickness of the front large flap.
The bottom left edge of this front large flap is a hinge edge that connects this large flap to a tapered triangular flap, which itself has a small free point corresponding to the rabbit ear.

Step 48.

Form a valley fold by bringing the bottom left edge of the front large flap along the vertical line marking the change in thickness.

Make sure to crease the fold well, then unfold.

Step 49.

Slide a finger between the two large symmetrical flaps.

Starting from the two valley folds made previously, make an outside reverse fold.

additional information

At this stage, the folding is quite complex, but the front and back flaps are still symmetrical.
There are four lower points facing 6 o'clock, one right point facing 3 o'clock, one top point facing 12 o'clock, and one left point facing 9 o'clock.
If you slide a finger inside the top point, you can feel the presence of the two small rabbit ear points.
We will refine the animal's front legs:
The animal's front legs correspond to the two lower left points.
A slightly oblique line marks a change in thickness at its legs.

Step 50.

Make a valley fold from left to right, along the line marking the change in thickness, from the lower left tip of the front flap.

Crease the fold well, then tuck the small folded end inside the leg.

Step 51.

Turn the folding over from right to left.

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the front legs of the animal now correspond to the two lower right points.

Step 52.

Make a valley fold from right to left, along the line marking the change in thickness, from the lower right tip of the front flap.

Crease the fold well, then tuck the small folded end inside the leg.

Step 53.

Turn the folding over from right to left.

additional information

at this stage the folding is quite complex, but the front and rear flaps are still symmetrical.
there are four lower points oriented at 6 o'clock, one right point oriented at 3 o'clock, one upper point oriented at 12 o'clock, and one left point oriented at 9 o'clock.
if you slide a finger inside the upper point, you can feel the presence of the two small rabbit ear points.

Step 54.

Form a horizontal valley fold along the hinge edge by folding the upper point down against the folded part.

Crease the fold well, then turn this valley fold into a mountain fold.

Crease well and then unfold.

Step 55.

Arrange the folding so that the four points initially oriented at 6 o'clock come into contact with the table, and the hinge edge is facing up.

Step 56.

Press on the hinge edge until its valley fold comes into contact with the table.

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there is a top left point, a top right point, a right point, a bottom right point, a bottom left point, a large left point, partially covered by two small left points.

Step 57.

Turn the folding from top to bottom.

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the horizontal axis of symmetry is marked by a valley slit.

Step 58.

Using the horizontal axis of symmetry, flip the top flap onto the bottom flap.

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we find the four bottom points oriented at 6 o'clock, the right point oriented at 3 o'clock, and a left point oriented at 9 o'clock.
the horizontal hinge edge connects the end of the right point to the end of the left point.
table side and ceiling side, a small tip pointing at 9 o'clock partially covers the left tip.

Step 59.

Lift the folding from the table and hold it in your hands in such a way that:

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The four tips previously pointing at 6 o'clock are now pointing toward the table, and the three tips previously pointing at 9 o'clock are now pointing to your left.
The four tips pointing toward the table will form the legs.
The 3 tips pointing to your left will become the head and ears.

Step 60.

Hold the folding between the thumb and middle finger of your right hand, at the animal's belly.

Step 61.

Place your left thumb against the left edge of the front flap, and your left index finger against the left edge of the back flap.

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The thumb and index finger of the left hand should be at the lower third of the left edges.
There is a slightly oblique valley fold on the left side of the front and back flaps.

Step 62.

Simultaneously push from left to right, using the thumb and index finger of the left hand, to fold down, using the existing slightly oblique valley folds, the left edges against the folding.