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Illustration of 16 congruent squares that have the same center. Each square has been rotated 5.625° in relation to the one next to it.

16 Congruent Rotated Squares

Illustration of 16 congruent squares that have the same center. Each square has been rotated 5.625°…

Illustration of 3 congruent squares that have the same center. Each square has been rotated 30° in relation to the one next to it.

3 Congruent Rotated Squares

Illustration of 3 congruent squares that have the same center. Each square has been rotated 30°…

Illustration of 6 congruent squares that have the same center. Each square has been rotated 15° in relation to the one next to it.

6 Congruent Rotated Squares

Illustration of 6 congruent squares that have the same center. Each square has been rotated 15°…

Illustration of 12 congruent squares that have the same center. Each square has been rotated 7.5° in relation to the one next to it.

12 Congruent Rotated Squares

Illustration of 12 congruent squares that have the same center. Each square has been rotated 7.5°…

Illustration of 2 concentric pentagons.

2 Concentric Pentagons

Illustration of 2 concentric pentagons.

Illustration of 2 concentric pentagons.

2 Concentric Pentagons

Illustration of 2 concentric pentagons.

Illustration of 3 concentric pentagons that are equally spaced.

3 Concentric Pentagons

Illustration of 3 concentric pentagons that are equally spaced.

Illustration of 4 concentric pentagons that are equally spaced.

4 Concentric Pentagons

Illustration of 4 concentric pentagons that are equally spaced.

Illustration of 2 regular congruent pentagons that have the same center. One pentagon has been rotated 36° in relation to the other.

2 Congruent Rotated Pentagons

Illustration of 2 regular congruent pentagons that have the same center. One pentagon has been rotated…

Illustration of 4 regular congruent pentagons that have the same center. Each pentagon has been rotated 18° in relation to the one next to it.

4 Congruent Rotated Pentagons

Illustration of 4 regular congruent pentagons that have the same center. Each pentagon has been rotated…

Illustration of 8 regular congruent pentagons that have the same center. Each pentagon has been rotated 9° in relation to the one next to it.

8 Congruent Rotated Pentagons

Illustration of 8 regular congruent pentagons that have the same center. Each pentagon has been rotated…

Illustration of a concave equilateral hexagon.

Concave Equilateral Hexagon

Illustration of a concave equilateral hexagon.

Illustration of 2 regular concentric hexagons.

2 Concentric Hexagons

Illustration of 2 regular concentric hexagons.

Illustration of 2 regular concentric hexagons.

2 Concentric Hexagons

Illustration of 2 regular concentric hexagons.

Illustration of 3 regular concentric hexagons that are equally spaced.

3 Concentric Hexagons

Illustration of 3 regular concentric hexagons that are equally spaced.

Illustration of 4 regular concentric hexagons that are equally spaced.

4 Concentric Hexagons

Illustration of 4 regular concentric hexagons that are equally spaced.

Illustration of 2 regular concentric hexagons with 6 congruent circles placed between the hexagons so that they are tangent to each other and both the inner and outer hexagons.

2 Concentric Hexagons With Tangent Circles

Illustration of 2 regular concentric hexagons with 6 congruent circles placed between the hexagons so…

Illustration of a regular hexagon with each side divided into thirds by line segments extended to the opposite side.

Regular Hexagon With Segments

Illustration of a regular hexagon with each side divided into thirds by line segments extended to the…

Illustration of 2 regular concentric heptagons/septagons.

2 Concentric Septagons/Heptagons

Illustration of 2 regular concentric heptagons/septagons.

Illustration of 2 regular concentric heptagons/septagons.

2 Concentric Septagons/Heptagons

Illustration of 2 regular concentric heptagons/septagons.

Illustration of 3 regular concentric heptagons/septagons that are equally spaced.

3 Concentric Septagons/Heptagons

Illustration of 3 regular concentric heptagons/septagons that are equally spaced.

Illustration of 4 regular concentric heptagons/septagons that are equally spaced.

4 Concentric Septagons/Heptagons

Illustration of 4 regular concentric heptagons/septagons that are equally spaced.

Illustration of a concave equilateral octagon.

Concave Equilateral Octagon

Illustration of a concave equilateral octagon.

Illustration of a regular octagon circumscribed about a square. This could also be described as a square inscribed in a regular octagon.

Octagon Circumscribed About a Square

Illustration of a regular octagon circumscribed about a square. This could also be described as a square…

Illustration of 2 regular concentric octagons.

2 Concentric Octagons

Illustration of 2 regular concentric octagons.

Illustration of 2 regular concentric octagons.

2 Concentric Octagons

Illustration of 2 regular concentric octagons.

Illustration of 3 regular concentric octagons that are equally spaced.

3 Concentric Octagons

Illustration of 3 regular concentric octagons that are equally spaced.

Illustration of 4 regular concentric octagons that are equally spaced.

4 Concentric Octagons

Illustration of 4 regular concentric octagons that are equally spaced.

Illustration of 2 regular concentric nonagons.

2 Concentric Nonagons

Illustration of 2 regular concentric nonagons.

Illustration of 2 regular concentric nonagons.

2 Concentric Nonagons

Illustration of 2 regular concentric nonagons.

Illustration of 3 regular concentric nonagons that are equally spaced.

3 Concentric Nonagons

Illustration of 3 regular concentric nonagons that are equally spaced.

Illustration of 4 regular concentric nonagons that are equally spaced.

4 Concentric Nonagons

Illustration of 4 regular concentric nonagons that are equally spaced.

Illustration of a rhombus circumscribed about an ellipse. This could also be described as an ellipse inscribed in a rhombus.

Rhombus Circumscribed About an Ellipse

Illustration of a rhombus circumscribed about an ellipse. This could also be described as an ellipse…

Illustration of an equilateral triangle inscribed in an equilateral triangle. The smaller triangle is created by joining the midpoints of the sides of the larger triangle. The area of the inscribed triangle is 1/4 the area of the larger triangle.

Equilateral Triangle Inscribed In An Equilateral Triangle

Illustration of an equilateral triangle inscribed in an equilateral triangle. The smaller triangle is…

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints of the sides of the larger triangle. 3 smaller equilateral triangles are then constructed in the remaining area by joining the midpoints of the other 3 triangles.

Equilateral Triangles Inscribed In An Equilateral Triangle

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints…

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints of the sides of the larger triangle. Thus, there are 4 equilateral triangles inside of the large triangle. Inside each of the 4 smaller equilateral triangles another equilateral triangle is constructed by joining the midpoints of the sides.

Equilateral Triangles Inscribed In Equilateral Triangles

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints…

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints of the sides of the larger triangle. Inside the smaller equilateral triangle another inscribed equilateral triangle is constructed by joining the midpoints of the sides.

Equilateral Triangles Inscribed In Equilateral Triangles

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints…

Illustration of 2 concentric equilateral triangles.

2 Concentric Equilateral Triangles

Illustration of 2 concentric equilateral triangles.

Illustration of 2 concentric equilateral triangles.

2 Concentric Equilateral Triangles

Illustration of 2 concentric equilateral triangles.

Illustration of 3 concentric equilateral triangles that are equally spaced.

3 Concentric Equilateral Triangles

Illustration of 3 concentric equilateral triangles that are equally spaced.

Illustration of 4 concentric equilateral triangles that are equally spaced.

4 Concentric Equilateral Triangles

Illustration of 4 concentric equilateral triangles that are equally spaced.

Illustration of an equilateral triangle that shows both the centroid (where the medians of the sides meet) and the incenter (where the angle bisectors meet).

Centers of Equilateral Triangle

Illustration of an equilateral triangle that shows both the centroid (where the medians of the sides…

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been rotated 12° in relation to the one next to it. The outer vertices are connected with a smoother curve to form a circle. Hence, the circle is circumscribed about the triangles.

10 Congruent Rotated Equilateral Triangles

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been…

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been rotated 12° in relation to the one next to it.

10 Congruent Rotated Equilateral Triangles

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been…

Illustration of 5 congruent equilateral triangles that have the same center. Each triangle has been rotated 24° in relation to the one next to it.

5 Congruent Rotated Equilateral Triangles

Illustration of 5 congruent equilateral triangles that have the same center. Each triangle has been…

Illustration of 20 congruent equilateral triangles that have the same center. Each triangle has been rotated 6° in relation to the one next to it.

20 Congruent Rotated Equilateral Triangles

Illustration of 20 congruent equilateral triangles that have the same center. Each triangle has been…

Illustration of a 12-point star (24-sided polygon) inscribed in a regular dodecagon. This can also be described as a regular dodecagon circumscribed about a 12-point star (24-sided polygon).

12-Point Star Inscribed In A Dodecagon

Illustration of a 12-point star (24-sided polygon) inscribed in a regular dodecagon. This can also be…

Illustration of a closed concave geometric figure with 16 sides in the shape of a 8-point star.

8-Point Star

Illustration of a closed concave geometric figure with 16 sides in the shape of a 8-point star.

Illustration of a closed concave geometric figure with 18 sides in the shape of a 9-point star.

9-Point Star

Illustration of a closed concave geometric figure with 18 sides in the shape of a 9-point star.

Illustration of a closed concave geometric figure with 20 sides in the shape of a 10-point star.

10-Point Star

Illustration of a closed concave geometric figure with 20 sides in the shape of a 10-point star.

Illustration of a closed concave geometric figure with 24 sides in the shape of a 12-point star.

12-Point Star

Illustration of a closed concave geometric figure with 24 sides in the shape of a 12-point star.

Illustration of an equilateral triangle inscribed in a closed concave geometric figure with 24 sides in the shape of a 12-point star. The two figures are concentric.

Triangle Inscribed In A 12-Point Star

Illustration of an equilateral triangle inscribed in a closed concave geometric figure with 24 sides…

Illustration of a square inscribed in a closed concave geometric figure with 24 sides in the shape of a 12-point star. The two figures are concentric.

Square Inscribed in a 12-Point Star

Illustration of a square inscribed in a closed concave geometric figure with 24 sides in the shape of…

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a circle circumscribed about a pentagon. In this illustration, the pentagon is not regular (the lengths of the sides are not equal).

Cyclic Pentagon

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a…

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described as a circle circumscribed about a quadrilateral. In this illustration, the quadrilateral is not regular (the lengths of the sides are not equal).

Cyclic Quadrilateral

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described…

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle circumscribed about a hexagon. In this illustration, the hexagon is not regular (the lengths of the sides are not equal).

Cyclic Hexagon

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle…

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle circumscribed about a hexagon. In this illustration, the hexagon is not regular (the lengths of the sides are not equal).

Cyclic Hexagon

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle…

Illustration of an 8-point star, or convex polygon, inscribed in a circle. This can also be described as a circle circumscribed about an 8-point star.

Star Inscribed In A Circle

Illustration of an 8-point star, or convex polygon, inscribed in a circle. This can also be described…

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about a smaller circle.

Star Inscribed And Circumscribed About Circles

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about…

Illustration of an 8-point star (convex polygon) circumscribed about a circle. This can also be described as a circle inscribed in an 8-point star, or convex polygon.

Star Circumscribed About A Circle

Illustration of an 8-point star (convex polygon) circumscribed about a circle. This can also be described…