We will now move onto two geometrical symbols of the Heptad. One is 2D – the heptagon and heptagram.

The other is 3D – the 7-sided figure called the Chestahedron, discovered in modern times by artist and geometrician Frank Chester.

# The Heptagon – 900º

The heptagon is seven-sided regular polygon.

Each interior angle = 51.4128571…°

Each exterior angle = 128.57….°

The sum of angles = 900º.

900 hertz = A# (the note required to complete F# major chord in perfect harmony).

The heptagon cannot be perfectly constructed with the geometer’s tools. It is the only one with this property within the decad.

However, approximations are possible to construct.

*Credit: Michael Schneider – A Beginner’s Guide to Constructing the Universe*

Interior angle = 51.4128571…..°

Seven is the only number (within the decad) that does not divide evenly into 360.

It produces and endless decimal. It cannot be captured.

Number |
Center Angle |
Vertex Angle |

1 | 360 | Infinite |

2 | 180 | 0 |

3 | 120 | 60 |

4 | 90 | 90 |

5 | 72 | 108 |

6 | 60 | 120 |

7 | 51.4128571… |
128.571428… |

8 | 45 | 135 |

9 | 40 | 140 |

10 | 36 | 144 |

# Area of the Heptagon

A = (__7__a^{2})4 x (cot[__180º])/7__ where a = side length

The Heptagon is a symbol of eternal, rather than manifest things.

Reference Construction Lesson #69: Constructing the Heptagon

# Heptagrams

There are two stellations of the heptagon, or two types of seven-pointed stars.

The first is constructed by connecting every other point of the heptagon (skipping 1 point).

The second is constructed by connecting every 3^{rd} point (skipping 2 points) of the heptagon.

“A heptagram imparts a feeling of movement because our eye attempts to resolve the unevenness of the form. We sense its elusive eternal character as motion. The number seven represents the most direct link with archetypal patterns accessible to us in symbolic form.”1

# The “Web of Athena”

Both heptagrams within one heptagon produces the “Web of Athena”.

It is composed of 3 line lengths.

# Division of a Circle in Seven Parts

A rhomb can be used as a template to divide a circle into 7 equal parts. This rhomb is seen below in red.

This is seen in the Bronze Age Clandon Barrow gold breastplate found in Dorset, England and discussed in detail in Keith Critchlow’s* Time Stands Still*.

*Credit: Silent Earth*

The rhomb is 102 ¾º. When placed on the center of a circle it divides the circle into 2/7 to an accuracy of less than ¼ of a degree.

# Sound of Seven

You can hear what a heptagon sounds like if you construct a heptagon on wood and hammer nails part way into the wood at three points (shown below in bold black) and tie a piece of guitar string or piano wire around the nails, using equal tension.

You can find their tone from high to low.

Listen to the intervals and jumps they make.

Pluck two strings simultaneously and listen to the rhythmic beat arising in their differences.

# The Chestahedron – Seven-Sided Polyhedron

We have mentioned the seven-side polyhedron, the Chestahedron, several times in previous articles. We will reiterate that information here.

The Chestahedron was discovered by Frank Chester in 2000. Frank Chester is an artist, sculptor, teacher and geometrician based in San Francisco.

The Chestahedron is a 3-fold rotational prismatic symmetrical heptahedron.

It is the first known seven-sided solid with faces of equal area.

It has:

- 7 Faces (4 equilateral triangles; 3 quadrilaterals (kites))
- 7 Points
- 12 Edges

It has 4 vertices with 3 edges meeting and 3 vertices with 4 edges meeting.

It’s Surface Area has 7 equal faces.

The Chestahedron has the following Dihedral Angles:

- 75 quadrilateral to quadrilateral
- -94.83 triangle to triangle
- 30 quadrilateral to triangle

# The Net of the Chestahedron

Its Dual is the Dekatria, a 13-sided figure also discovered by Frank Chester.

The Chestahedron can be harmonically integrated into a cube when it is oriented at an angle of 36 degrees.

*Credit: Frank Chester. The angle of 36 degrees was noteworthy to Mr. Chester because he remembered that the human heart sits at that particular angle inside of a person’s chest.*

The Chestahedron offers a new perspective on art, sculpture, architecture, the form and function of the human heart and the interior of the Earth.

# The Chestahedron can be formed through a vortex motion of the dodecahedron, tetrahedron and octahedron:

## The Pentagonal Face of the Dodecahedron:

The two-dimensional, unfolded version of the Chestahedron relates exactly to a perfect five-pointed star.

One of the kite shapes equals 1/5 of a pentagram. This is shown in red.

Five of the kite shapes, placed with their points together, makes the star pentagon.

This means the Chestahedron can be created by folding up a star pentagon on itself, bringing it into three dimensions.

It also relates to the icosahedron and dodecahedron.

The fundamental uniting factor is the base equilateral triangle.

*Credit: Frank Chester*

## The Chestahedron can be created in Two Distinct Ways from a Tetrahedron:

### First way: Contractive

Place a tetrahedron inside a cube, and while keeping the boundaries of the cube inviolate, twist the tetrahedron so that one of its points moves along the diagonal of one square face to the opposite corner.

The tetrahedron, at this point, has changed into the octahedron.

There are actually 2 moments, between the transformation of the tetrahedron into the octahedron, that result in the Chestahedron.

The geometry of the Chestahedron is a geometry of motion (vortex motion). It represents a process of life rather than a ‘part’ or object in life. Remember, the Heptad symbolizes processes, not things.

The Chestahedron itself is merely a balanced moment of rest in a whole field of geometric activity that involves all of the Platonic forms.

*Credit: Seth Miller*

### Second way: Expansive

This begins with the tetrahedron, which is then unfolded like a flower with three petals.

See this in detail at: www.frankchester.com/2009/chestahedron-from-a-tetrahedron/.

The opening of the tetrahedron immediately creates the seven-sided form with the addition of the three kite-shaped faces.

It only remains to unfold the petals to the exact angle at which the area of the kite faces equals the area of the equilateral triangles at angle 94.83.

This unfolding sequence, traced through time, can be taken further.

If the unfolding of the petals continues past the point at which the Chestahedron arises, a moment comes when the dihedral angle becomes 109.47.

At this moment it takes the shape of a perfect octahedron with a tetrahedron on top that is exactly the size of the original tetrahedron.

This whole form itself is bounded by a tetrahedron that is exactly twice the size of the original.

As we have been examining all throughout Cosmic Core, all in life and reality is based upon a geometric matrix that is made up of the regular polygons, five Platonic Solids and 13 Archimedean solids, as well as all the various truncations, stellations, combinations and transition states of these forms.

The Chestahedron is a perfect example of what geometry can be formed from through a transitional shape of the Platonic solids.

It is helpful to remember that All is Motion. So even though we think of geometry as static figures and forms, in reality, geometry is continually pulsing, oscillating, spiraling and transforming from one shape to another to another, and so on…

# Geometry of the Human Heart Related to the Chestahedron

The geometry of the Chestahedron includes the positioning of the heart in the chest cavity and the actual geometry of the heart itself, particularly the shape and relative sizes of the left and right ventricles.

When spun, the Chestahedron traces out a unique bell shape.

The bell shape, when spun in water at an angle equivalent to the angle at which the heart sits in the chest, produces a vortex that has a uniquely-shaped cavity that appears around the form.

A cross-section of the bell and cavity strongly resembles the cross-section of a human heart.

It also relates to:

- the orientation of the successive layers of the heart’s muscles
- the relative thickness of the ventricle walls
- the size of the ventricle openings
- the shape of the whole heart
- the extreme thinness of the heart’s apex
- the vortexial motion of the heart and the blood inside it
- and how all this relates to the Vesica Piscis and the square root of 3

See Article 196 for more information on the Chestahedron in relation to the human heart.

As Frank Chester writes, “the formative forces which form our heart muscle are active as vortices and are oriented and maintained through the seven-sided form.”

“The heart is no longer a pump. It has instead become an organ of flow (regulation). If the heart were a pump, the paper-thin tissue at the apex of the left ventricle could never withstand the developing pressure. However, from the perspective of a vortex model of the heart, it becomes understandable why this part of the heart is never exposed to these higher pressure dynamics.”2

*The Seven Layers of the Human Heart. Credit: Frank Chester*

“In the developing human embryo, blood is already streaming rhythmically through its blood vessels before the heart has even formed. Something other than the heart, therefore, must be responsible for this movement of the blood. The heart that develops later appears to function more like a balancing brake: blood streams into the left ventricle in a clockwise direction and then vortexes around itself, finally emerging from the left ventricle in the opposite, counter-clockwise direction. At the moment when the blood flow reverses, there is no movement; absolute stillness reigns. However, this is a dynamic rest. This is the exact moment, simultaneous in time and space, that for Frank Chester represents the eternally present heart-centered state in each human being.”3

# The Chestahedron’s Relationship to the Earth

See: http://www.frankchester.com/2010/the-mysterious-heart-das-goetheanum-article/ for more information.

*The Chestahedron in the Earth. Credit: Frank Chester*

Frank Chester found a number of relationships with respect to the size of the inner and outer cores of the Earth including:

- the placement of the auroras
- and the relative size of the core of Earth and moon

The Earth has both an inner and outer core; together they form a sphere 6972 km in diameter. The Moon has a diameter of 3474 km, which is almost exactly half that of the Earth’s core (~99.7% accuracy). In other words, two Moons, side by side fit exactly into the Earth’s core.

“The Chestahedron acts as a fundamental geometric form within our earth. If one follows a lawful transformation involving surface-point-surface mapping, it can be shown that the Chestahedron has a cube as its foundation (within it). With reference to the dimensions of the earth, this cube has the same diameter as our moon (the earth’s core has a diameter of 3400 km; the diameter of the moon is 3474 km). In 2008, scientists at Uppsala University in Sweden published findings that appeared to confirm that the core of the earth is a cube (Translator note: Specifically, the round earth’s core has a cubical iron crystalline structure and not a hexagonal one as assumed in older models).

These findings, which are aligned with the idea of a Chestahedron in the earth, offer an explanation why seismic waves travel (through the core) faster along the Earth’s axis (from pole to pole) in comparison to their movement from equator to equator. It can also be shown that notable synchronic lines that join regions of cooler, warmer, and hotter earthly zones in seismic maps correspond essentially to the suggested Chestahedron model within the Earth.

Perhaps the most impressive application of this work may be an explanation for the underlying phenomenology in the appearance of the northern lights: The distribution in the appearance of both the northern lights (aurora borealis) and the southern lights (aurora australis) (on the earth’s surface seen from space) appear to be in alignment with the rings that Frank Chester found in his experiments with the Chestahedron creating water vortices while studying the energetic origin of the human heart. Using the Chestahedron, Chester found a common denominator, a starting point which promises to offer a deeper understanding of both earthly phenomena as well as those of the human heart.”4

- Schneider, Michael,
*A Beginner’s Guide to Constructing the Universe*, Harper Perennial, 1994 *The Heart is a Sacred Geometry Vortex*, http://humansarefree.com/2014/09/the-heart-is-sacred-geometry-vortex.html- ibid.
- http://www.frankchester.com/2010/the-mysterious-heart-das-goetheanum-article/

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