viernes, 31 de octubre de 2014

The Flexagon Portal

The Flexagon Portal
Flexagon.net was created to provide a place for all those interested in flexagons to share their ideas, templates, or anything related to flexagons. Here is what you will find:
  1. Original flexagon templates - For some of the templates, each triangle or polygon unit is separately labeled and every corner coded.  This allows one to more easily discover all the combinations of faces and rotations of the polygons.
  2. Information on technical aspects of flexagons and on creating flexagons.
 Flexagons continue to stimulate interest from recreational mathematicians, artists, paper folders, and even from serious mathematicians.  Check out the great templates below.  Please feel free to give me comments from the contact page.  I am also a member of the Yahoo Flexagon group .
Note:  The following templates are free for personal or classroom use. Anyone that wants to use these for publications either written or Internet, must contact me for approval. (see Contact Me tab)

Trihexaflexagon
Classic

 trihexaflexagon
This is the classic 3 faced hexaflexagon.  This template is created to be easy to cut out, glue and fold up.  This fresh design has been nicely labeled to best show off the mathematical properties of the flexagon.  Everyone should make one of these!

Tetrahexaflexagon 

tetrahexaflexagon
This flexagon is not nearly as widely known and folded, but it is almost as easy to cut out and fold up as the classic.  The four faces provide opportunity for design creativity. A well folded model will flex very smoothly with well formed faces.

Pentahexaflexagon

Hexahexaflexagon
Variatiion A

hexahexaflexagon

Hexahexaflexagon
Variation B

hexahexaflexagon

Hexahexaflexagon
Variatiion C

hexahexaflexagon

The Snake
Heptahexaflexagon
Variation A

heptahexaflexagon

 

Heptahexaflexagon
Variation B & C

heptahexaflexagon
 
Template for the B and C variations of the 7 faced heptahexaflexagon.  Both variations are folded from the same template.  Within each folded variation, you can see the faces of the other variation.  Be sure to check out the "G" and Sunday face on both variations.  Challenge - Can you V-flex from one variation to the other?  This is the hexaflexagon with the smallest number of faces that will fold up into two flexagons with different Tuckerman state diagrams.
 

Fire and Wood
Heptahexaflexagon
Variation D - Now available for Download!


heptahexaflexagon 4
 
Template for the D and last variation of the 7 faced heptahexaflexagons. This is the hexaflexagon with the smallest number of faces where the template curls on top of itself.  In fact the template has three spirals in it.  This flexagon is a bit more challenging than the others on this page to make due to the more complex template.  One of many interesting things about this flexagon is that if you start with the E face on top and the F face on the bottom, you can flex 5 times from the same corner.  Give it a try.

Native Animal Symbols

Title


AlligatorAlligator:
Aggression, survival, adaptability
Ant:
Group minded, perseverance, step by step.
The ant represents self discipline and a group effort.
Teamwork.
Ant
batBat:
Guardian of the night, cleaner
Bear:
Power, mother cunning, healer, gentle strength, dreaming.
In the Zuni tradition, the bear symbolizes the direction West.
Black Bear
BeaverBeaver:
Builder, gatherer
Buffalo:
Sacredness, life builder.
The buffalo provides all good things
for living, and bestow's great curing powers
Buffalo
ButterflyButterfly:
Metamorphosis, carefree, transformer
Cougar:
Leadership, courage, power, swiftness and balance.
Cougar
coyoteCoyote:
Prankster, insight, playful. The coyote
symbolizes duality and the ability
to present both sides of an issue.
Clowning and humor, perhaps sarcastic.
Crane:
Solitude, independence
Crane
DeerDeer:
Love, gentleness, kindness, gracefulness
and sensitivity. Deer carries
the message of purity of purpose,
and of walking in the light.
Dolphin:
Kindness, play, bridge man to ocean.
Dolphin brings us teachings from the water.
Breath control and the awareness of
tone is also Dolphin power.
Dolphin
Dragon FlyDragonfly:
Flighty, carefree. Dragonflies symbolize whirlwind,
swiftness and activity. The dragonfly is
an important insect in Zuni legend, where they are
shamanistic creatures with supernatural powers.
In Hopi rock art, the dragonfly is symbolized by a
vertical line with two or sometimes one,
horizontal cross line.
Eagle:
Divine spirit, chief of all the creatures in the air,
the primary servant of the sun. Powerful in battle,
the eagle protects the people from evil.
Eagle medicine attributes
include clear vision and soaring spirit.
The eagle is associated with success,
prosperity and wealth. In the Zuni Tradition,
the Eagle symbolizes the direction Up.
Eagle
ElkElk:
Strength, agility, freedom, power and nobility.
Fox:
Cunning, provider, intelligence.
Fox represents twilight and feminine magic.
Red Fox
FrogFrog:
Connection with water element
Grizzly Bear:
Mother, nature's pharmacist
Grizzly Bear
HawkHawk:
Messenger of the sky, observer
Horse:
Stamina, mobility, strength and power.
The horse was introduced to the plains tribes by the Spanish.
Shaman's are often pictured flying on mythical horses.
Horses can symbolize coping under difficult circumstances.
Horse is love and devotion, loyalty.
Horse
Humming BirdHumming Bird:
Messenger, stopper of time.
Hummingbird represents optimism and sweetness.
Being able to roll with the punches
is an attribute of Hummingbird.
Lizard:
Conservation, agility.
Lizard promotes dreaming.
Green Skink
MooseMoose:
Headstrong, unstoppable longevity.
Moose represents value and integrity.
Otter:
Laughter, curiosity, mischievous.
Otter is a feminine power,
and the symbol of grace and empathy.
Otter
Great Grey OwlOwl:
Wisdom, truth, patience.
The Mescalero believe that Owl carries the
souls of the recently deceased, a death messenger.
Owl is the totem of clairvoyants and mystics.
Rabbit:
Alertness, nurturing
Rabbit
RavenRaven:
Trickster, teacher, hoarder.
To Pacific Northwest Coast tribes, Raven represented the
shaman's powers and a belief in transformation between
human and animal spirits. Raven symbolizes change in
conciousness and is the mark of a shape shifter.
Salmon:
Instinct, persistence, determination
Salmon, swimming upstream
SeahorseSeahorse:
Confidence, grace
Shark:
Hunter, survival, adaptability
Shark
Rattle SnakeSnake:
Shrewdness, transformation.
Life, death and rebirth are represented by
the shedding of skin. Among the Pueblo Indians
snakes and lightning are equated with rain and fertility.
Spider:
Creative, pattern of life.
Spider connects the past with the future, creating possibilities.
Spider-woman is a major Pueblo goddess
Tarantula Spider
SwansSwan:
Grace, balance, innocence
Turtle:
Self contained, creative source.
Turtle represents Mother Earth.
Informed decisions, planning and adaptability
are attributes of Turtle.
Turtle
WolfWolf:
Loyalty, success, perseverance, stability and thought.
Wolves are also regarded as path finders and teachers.
Wolf is represented by the constellation Sirius, the Dog.
In the Zuni tradition the Wolf symbolizes the direction East.
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