Hyperbolic Orthogonal Dodecahedral Honeycomb

Bincuntracated Cubic Tiling

Fourth-Dimensional Hypercube

This is what a fourth-dimensional hypercube looks like as visualized from a three-dimensional perspective.

Hypercubes in other dimensions

The Platonic Solids

The Platonic Solids

Tetrahedron


The exact projection of a Tetrahedron onto a sphere




Hexadron (Cube)


The exact projection of a Hexahedron (Cube) onto a sphere



Octahedron


The exact projection of a Octahedron onto a sphere




Icosahedron


The exact projection of a Icosahedron onto a sphere




Dodecahedredon


The exact projection of a Dodecahedron onto a sphere


Higher Dimensions of the Platonic Solids
In the mid-19th century the Swiss mathematician Ludwig Schläfli discovered the four-dimensional analogues of the Platonic solids, called convex regular 4-polytopes. There are exactly six of these figures; five are analogous to the Platonic solids, while the sixth one, the 24-cell, has no lower-dimensional analogue.

In dimensions higher than four, there are only three convex regular polytopes: the simplex, the hypercube, and the cross-polytope. In three dimensions, these coincide with the tetrahedron, the cube, and the octahedron.

It's not about others

It is not the shortcomings of others, nor what others have done or not done that one should think about, but what one has done or not done oneself.
The Dhammapada, Verse 50

A prayer for happiness

My all beings have happiness and the causes of happiness.
May all beings be free from suffering and the causes of suffering.
May all beings never be separated from the happiness free from suffering.
May all beings have equanimity, free from attachment and aversion.

Overcoming Death Mandala

from "the art of asia," minneapolis institute of arts:

Yamantaka Mandala (Overcoming Death Mandala)

A mandala, or circle, is a representation of the Buddhist universe. These cosmograms represent in symbolic color, line, and geometric forms, all realms of existence and are used in Tantric meditation and initiation rites. The creation of a mandala, considered a consecrated area, is believed to benefit all beings.

This is the Yamantaka mandala, a cosmic blueprint of the celestial palace of the deity Yamantaka, Conqueror of Death, who is represented at the center by the blue vajra, or thunderbolt. It consists of a series of concentric bands, the outermost representing eight burial grounds with a recognizable landscape and animals symbolizing our earthly plane of existence. Moving inward are a circle of flames, a circle of vajras, and a circle of lotus petals. These bands circumscribe a quadrangle with gates at the four compass points, suggesting the realm of form without desire. The innermost square is divided into triangular quadrants, and an inner circle is subdivided into nine units containing symbols representing various deities. This is the realm of absolute formlessness and perfect bliss. In the four outside corners are the attributes of the five senses (smell, sight, sound, taste, and touch), reminders of the illusory nature of our perceived reality.

All mandalas represent an invitation to enter the Buddha's awakened mind. Tibetan Buddhists believe there is a seed of enlightenment in each person's mind; this is uncovered by visualizing and contemplating a mandala. The complex symbols and exquisite combination of primary colors are considered a pure expression of the principles of wisdom and compassion that underlie Tantric Buddhist philosophy.

This mandala was created to honor the 1.2 million Tibetans who have lost their lives to political/religious persecution during this century.

The museum thanks the Tibetan American Foundation of Minnesota for bringing the Gyoto monks to Minnesota and for their efforts to preserve Tibetan cultural traditions.

What is a Seraph?

The following is a mash-up of information I found on the internet:

A seraph (plural, seraphim) is one of a class of divine creatures or celestial beings. The root word comes either from the Hebrew verb saraph ("to burn") or the Hebrew noun saraph ("a fiery flying serpent"). The term saraph appears several times in the Old Testament, with reference to the serpents encountered in the wilderness. It has often been understood to refer to "fiery serpents." From this it has also often been proposed that the seraphim were serpentine in form and in some sense "fiery" creatures or associated with fire.

Seraphim are described as very tall, generally having the figures of men, with six wings and four heads (one for each of the cardinal directions). One pair of wings are for flying, one for covering their eyes (for even they may not look directly at God), and one for covering their feet.

Seraphim serve and are in the direct presence of God. It is said that whoever lays eyes on a seraph would be instantly incinerated due to their immense brightness. [Do you remember the final scene in "Raiders of the Lost Ark" in which the Nazis were consumed by fire? They foolishly dared to look at the seraphim protecting the Ark of the Covenant.]

Later Jewish imagery perceived seraphim as having human form, and in that way they passed into the ranks of Christian angels. In the Christian angelic hierarchy, seraphim represent the highest rank of angels.

King James Bible, Isaiah 6: 1-2 "In the year that king Uzziah died I saw also the Lord sitting upon a throne, high and lifted up, and his train filled the temple. Above it stood the seraphims: each one had six wings; with twain he covered his face, and with twain he covered his feet, and with twain he did fly."

The Mandala of Seven Seraphim

The Bodhisattva Mañjushrî

Mañjushrî is an ancient Buddha who vowed to emanate throughout the universe as the always youthful, princely Bodhisattva of Transcendent Wisdom. His special purpose is to lead the audiences of the Buddha in the inquiry into the self, to discover the true nature of reality. He is usually depicted holding the text of the Transcendent Wisdom (Prajnaparamita) Sutra in his left hand and the double-edged sword of analytic discrimination, which cuts through all delusions, in his right.

Mañjushrî raises his hands in front of his heart in the teaching gesture. He sits comfortable in the pose of ease atop an ornate lotus pedestal whose base is decorated with winding vines and cavorting lions, probably a reference to the lion mount he sometimes rides.

Mañjushrî carries with his right hand the double edged sword able to cut through illusion and with his left hand a blooming lotus that supports a volume of the Prajnaparamita Sutra. He is depicted as a youth of sixteen years in order to convey the Buddhist insight that wisdom is not a matter of mere experience or years, but results from the cultivation of intellectual genius, which can penetrate directly to the bedrock of reality.

Wisdom is considered the most honoured virtue in Buddhism, called the Mother of all Buddhas, since only wisdom makes possible the great bliss of total freedom from all suffering that is the goal all living beings. Thus, Mañjushrî is one of the most important of all Buddhist deities.

Manjushri's mantra:
Om A Ra Pa Ca Na Dhih

This mantra has absolutely no conceptual meaning. The syllables are the first syllables of each line of the Avatamsaka Sutra, which is a text concerned with the Perfection of Wisdom (Prajñaparamita).

Pronunciation notes:
a is pronounced as u in cut
c is like ch in church
ii is like ee in bee
The final h in dhiih has the effect of producing an echo sound. So the syllable is pronounced dhii-hii.

Seeing Paramahansa Yogananda on film

this is a silent film


this is a talking film
Self Realization Fellowship

A disciple of Yogananda keeps it simple

Center for the Study of Awareness

In Search of the Garudas

This is a traditional Tibetan image of the Red Garuda.

This description of garudas follows from the The Symbols of Tibetan Buddhism page:

"The Garuda is daring and fearless and abides in the north. With great strength and power it soars beyond without holding back. It symbolizes freedom from hopes and fears, the vast mind without reference point. It is a powerful antidote to the negative influences of Nagas (spirits) which can cause disease and all kinds of harm."


Ogyen (Green) Garuda.
This is a description of the Green Garduda (Ogyen Garuda):

"Ogyen Garuda is Padmakara in the form of the immense space eagle who is born fully enlightened and in full flight. His furious gaze burns away the fabric of duality for all beings, conditions, and situations. His brilliant blue complexion reflects his spacious intelligence and the vast expanse of Dharmata. His hair is a roaring mass of wisdom-fire, which scorches the perceptual distortions of monism, dualism, nihilism, and eternalism. His two meteorite iron horns impale the deluded division of samsara and nirvana. His golden razor beak bites through every dualistic contrivance, and his two wings bear him beyond the limited spaces of existence and non-existence. The nine-fold pinions of his razor wings liberate beings in the temporal spaces of the nine bardos. He wears the human bone ornaments which display the spatial essence of the six classes of Vajrayana. At the centre of his chest ornament is the luminous green 'Trom' which illuminates the universe and makes total collision with reality inescapable.

In each hand he holds a nine-pronged meteorite iron phurba. These two phurbas liberate the potential of the solar and lunar channels and overpower all apparent phenomena in empty rage. With his two phurbas he stabs attraction, aversion, and indifference as they pertain to clinging either to samsara or nirvana. In each claw he holds a nine-pronged beryllium copper grigug. These two grigugs slash the fabric of dualistic clinging in every dimension of existence simultaneously -- without need of moving from the vast single point of awareness."

The Dark Blue Garuda.

Garudas are terrifying

The Garuda is the traditional mount of Lord Vishnu.

Garudas in Hinduism and Buddhism

"Garuda" in Wikipedia

Define "Judgment"

This is a post from my tribes friend Viveka.

Om jai Kindred Spirit… jai onto all

It is only by entering the darkness that one becomes fully enlightened; realizing we are the light we seek, and remembering that we really never left our humble abode beloved of Eternal Truth and Perfect Love behind.

Eternal Truth & Perfect Love is who we really are without the clothing of Maya.

If defining and judging the reality we see around us, helps us to remember Spirit, and moves us closer to the goal of Truth one seeks… We can say we are in Truth, we abide in the light, and it is good karma… If defining and judging the reality we see around us, moves away from the goal of Truth one seeks and, causes us to forget our divinity… We are not in Truth; we abide in darkness, and this is bad karma.

Bad karma leads to pain and suffering, and good karma leads to the eternal bliss of wellbeing. There is a time and a moment for everything within Maya. Maya is the seeming wondrous illusion of separation in beautiful yin/yang balance that helps us remember what we have forgotten. While we are clothed in Maya, with our costumes of name and form; we must explore both good and bad karma to fully understand the nature Eternal Truth & Perfect Love. We need both good & bad, light & darkness, hot & cold, so as to compare one with another to understand the nature both. Good and bad are two sides of the same coin. What gives value to a coin is the metal between the two sides, and so it is with the pair of opposites in yin & yang balance… The nature of Eternal Truth is found in that eternal moment between tick & tock, and the balance of yin & yang.

When we enter the darkness we forget.
We forget in order to sing God’s glory in the remembering.
We forget in order to honor the source of our being, through the cosmic karmic journey of awakening we are all on, transforming the darkness back into light.

When we move away from our center of truth, it is best to abide in seeming dark silence not judging the world around us, so that we find our center of truth, and better see where we are going with the singular vision of wisdom found in our heart… When we are centered in Truth within our heart, then it is time to open our eyes and express our divinity in all we do, as we explore and define the reality of Maya through the filter of viveka, honoring the source of our being.

We are the light; we are the seeming fragmented light that has entered the darkness to bring light to where light seems not to be; we come as an act of the highest devotion in motion honoring the source of our being.

It is most wonderful and beautiful how we are all expressing the same Eternal Truth from different points of view and in a different light, but the essence of the Eternal Truth we speak of, remains the same, unchanged and eternal.

JAI TO ALL YOU BEAUTIFUL LIGHTS, EXPRESSING ETERNAL TRUTH & PERFECT LOVE IN YOUR OWN UNIQUE WAYS!!! Thank you, for the wonderful contrast and beautiful colors that your individual and unique journeys of transformation add to our costume of Maya; which moves the heart to live life to the fullest.

Om shanti shanti shanti…

The Vedanta Society of Southern California

The Buddha Akshobya ("The Unshakeable")

OM VAJRA AKSHOBYA HUM

The Mandala of Buddha Akshobya

My enemy is my friend

The Mahayana Equilibrium Meditation, as instructed by Lama Zopa Rinpoche. Lama Rinpoche is the Spiritual Director of the Foundation for the Preservation of the Mahayana Tradition.

This meditation comes from Lama Zopa Rinpoche’s book, "The Wish-fulfilling Golden Sun of the Mahayana Thought Training" (Kopan Monastery, 1974). Rinpoche has described it as more than the standard equilibrium meditation, as he has added a number of techniques for overcoming anger and developing patience.

[Meditate in the first person and pause for contemplation between paragraphs.]


Think: It is never enough to gain only self-liberation. Attachment to personal peace and striving solely for this is both selfish and cruel.

Visualize that you are surrounded by all sentient beings, with your mother seated to your left and your father to your right. In front of you, visualize an enemy; someone who dislikes you or wishes you harm. Behind you, place your dearest friend; the person to whom you are most attached. To the side, visualize a stranger; someone for whom your feelings are neutral.

Think: There is no reason at all for me to be attached to and help my friend or to hate and harm my enemy.

If I were to strive for only my own self-peace, there would be no reason for me to have been born human. Even as an animal, I could strive for this. The various animals have the same aim as many highly educated people--self-happiness--and also create many negative actions, such as fighting with and destroying enemies, cheating others with political mind and so forth, all in the pursuit of their own happiness. There is almost no difference between them except their shape.

The main purpose of my having been born human is to strive for and achieve higher aims--to bring every sentient being to everlasting happiness. This is something no animal can ever do.

Just as I wish to avoid suffering and find happiness, so, too, do all other sentient beings. Therefore, I and all other sentient beings are equal, and there is no logical reason for me to care more about myself than others or to harm enemies or any other sentient being.

For countless rebirths I have been discriminating other beings as friend, enemy or stranger with the self-I consciousness. Chandrakirti said, “Where there is self-I consciousness, there is discrimination of other.” From discriminated partisanship between self and other, attachment and hatred arise.

All misfortune arises from acting under the influence of these negative minds.

The self-I consciousness causes attachment to self, which produces attachment to my own happiness.

The entire range of negative minds arises from the above.

Anger is caused by greed and self-attachment and makes me discriminate against whoever disturbs my happiness, producing the enemy.

Attachment creates the friend, who helps, and determines the enemy, who hinders.

Ignorance labels those who neither help nor hinder as strangers.

Anger makes me hate and harm the enemy; attachment makes me cling to and help the friend; and ignorance makes me see the stranger as having a permanent self-nature. By acting under the influence of these negative minds, I lead myself into difficult and suffering situations.

Attachment creates danger and suffering for myself and others. The whole earth is in danger of exploding. Attachment offers no peace and brings only suffering.

Since beginningless time, the two negative actions of helping out of attachment and harming out of anger have thrown me into samsaric suffering, making it impossible for me to achieve the perfect peace of liberation and enlightenment.

Negative actions leave negative imprints on the consciousness; these ripen into endless experiences of suffering. If I continue to behave in this way, I will experience the same suffering over and over again for eons and will never receive any realizations or enlightenment itself.

The three objects of friend, enemy and stranger are false and have been labeled incorrectly for extremely temporal reasons. The current friend, enemy and stranger have not always been friend, enemy and stranger in my countless, previous lives. Even the enemy of last year can this year become my friend and yesterday’s friend become my enemy today. It can all change within an hour and does so because of attachment to food, clothing and reputation.

A scripture says, “If you try for a moment to befriend an enemy, he will become your friend. The opposite occurs if you treat a friend like an enemy. Therefore, the wise, understanding the impermanent nature of temporal relationships, are never attached to food, clothing or reputation.”

Lord Buddha said, “In another life, the father becomes the son; the mother, the wife; the enemy, a friend. It always changes. In cyclic existence, nothing is certain.”

Therefore, there is no reason to be attached to friends or to hate enemies.

If the ignorant, self-I conception and its objects were true, the three designations of friend, enemy and stranger should have existed from countless previous lives and should continue to exist through the present to beyond enlightenment. This makes complete nonsense of the concept of enlightenment, since the Buddha’s sublime, enlightened mind is completely free of the delusions and imprints that create such distinctions.

Out of his compassion, Lord Buddha taught the equilibrium meditation so that I, too, might become free of delusions, imprints and ignorant discrimination. The concepts of friend, enemy and stranger are false because they and their basis are totally illusory. There is no self-I.

My problems are created not by the enemy but by me. In my previous lives, I harmed others through ignorance and the results of this return in this life, causing me hardship and suffering.

Lord Buddha said, “In previous lives, I have killed all of you before and you have all slaughtered me. Why should we now be attached to each other?”

Chandrakirti said, “It is foolish and ignorant to retaliate to an enemy’s attack with spite in hopes of ending it, as the retaliation itself only brings more suffering.”

Therefore, there is no reason to retaliate.

The enemy is the object of my practice of patience, which helps me overcome my anger. I should not hate this enemy, who brings peace into my mind.

The enemy is infinitely more precious than any material possession. He is the source of all my past, present and future happiness. I should never hate the enemy. Any possession can be given up for his peace.

An enemy is my greatest need, the source of all beings’ enlightenment, including my own. The enemy is my most precious possession. For his peace I can give up myself.

From now on I must never hate or harm the enemy or any other being.

The enemy harming me mentally and physically is under the control of his negative mind. He is like the stick that someone uses to beat another. There is no reason to get angry or to retaliate by harming the enemy. It is not his fault; just as the pain I experience from a beating is not the fault of the stick.

If I had clear wisdom I would see that harming others out of hatred is harming myself out of hatred. Obviously, I should not harm others.

All sentient beings, including the enemy, are the object of Lord Buddha’s compassion. The numberless buddhas hold the enemy and all other beings dear to their heart. Therefore, harming another, even slightly, is like harming the infinite buddhas.

The Buddha always considers all sentient beings, including enemies, to be more important than himself. Mindlessly harming another being for my own benefit is the act of a mind of stone.

The enemy and all other sentient beings have been my mother countless times. The holy body, speech and mind of the infinite buddhas are servant to all beings, enemies included. Therefore, I must never give harm to any other being.

Not harming my worst enemy, the ignorance in my mind, and destroying an outer enemy instead is like killing a friend by mistaking him for an enemy. I should not harm the outer enemy but the inner one, the actual cause of all my suffering.

Because of transcendent realizations based on the equilibrium meditation, no bodhisattva would ever see another sentient being as an enemy, even if all rose against him or her.

The enemy is merely a concept created by my hatred, just as friends and strangers are concepts created by my attachment and ignorance. I should not believe the distorted perceptions of my negative minds.

If I investigate with my wisdom eye, I will never find my attachment’s friend or my hatred’s enemy anywhere, neither inside nor outside their bodies. Wisdom tells me that these are merely names.

For all these reasons, I can now clearly see how foolish and nonsensical I have been over beginningless lifetimes.

If you could realize this equilibrium meditation it would be your most priceless possession. Equilibrium brings peace to numberless beings and all your future lives.

A tough question and a reluctant answer

On April 29th, a friend that I made on people.tribes.net, Lama Jime Gyatso, asked me a question that has been racing through my mind like a train through a subway tunnel.

>Lama-Jigme Gyatso wrote:
>
> Dear Daniel,
>
> Right now,
> in THIS moment;
> what are some of the specific things in your life
> that your heart could hunger to heal?
>
> Om Mani Padme Hum,
> Lama Jigme


It has taken me ten days to be able to come up with an answer.


Dear Lama Jigme,

I have been thinking of this question every day since you sent it to me. I am sorry that I have not responded sooner.

I was molested by a group of boys when I was five years old. I have spent years writing about it, sharing about it, being in therapy about it, praying and meditating about it, and suffering from it. There have been years when I thought the pain of it was going to drive me out of my mind. For 15 years, I tried to drink myself into oblivion over it. [Thank goodness I have been sober now for almost 20 years.]

For years I thought I was gay. At 30, I entered into my first gay relationship. It lasted for almost ten years. I thought "coming to terms" that I was "gay" would stop the pain. Instead, the pain just took a nap.

I have been on a three-year fast from sex, quieting my mind, hoping to discover the solution. Now I realize that thinking I was gay was a defense mechanism to not face the trauma of being essentially gang-raped. Believing that I had "asked for" being molested, I needed to think that I must be gay: that was how my little boy mind tried to comprehend what happened to me and why. Now I understand, that had I not been molested, I might not have ever thought of myself as gay. But that doesn't erase the experience.

I now regard myself as a straight man with a bisexual past and uncharted future. This, to me, represents a lot of healing and growth of consciousness. However, that has not removed the scars of the sexual trauma. I still feel a part of me wanders this earth, like a ghost, looking for a healing that I cannot conceive. Today I don't feel straight, gay, bisexual, or necessarily asexual; I don't fit in anywhere. Still feeling defensive, I think and behave like a sex-phobic sexual anorexic, as though that were going to cure me.

When I share this with most people, all of their sex phobias come up, and little to anything good comes of it. That just makes me feel more dislocated.

At various times in my life, I have lived as a monastic. Not surprisingly, those experiences did not address my sexual pain and shame. I have been a buddhist for a long time, but the pain remains.

I have run out of ideas what to do. But I think part of the problem is that I have been running on my old ideas. I have been running with those old ideas wrapped around me, not knowing what else to do.

Right now, in THIS moment, the thing that my heart is hungering to heal is my sexual trauma. I am not attached to what the consequences of this healing might be. What my heart hungers for healing is not about the sex; it's about my ability to connect with life and with others, who in many ways I have shut out.

Thanks for asking me this question. It's exhausted me, but I feel more heart conscious.

Sincerely yours, Daniel Jordan

Thanks for the question, Lama Jigme!

Link to Lama Jigme's web page.