#compound polyhedron

[knotty-et-al]

Dodecahedron and stellated dodecahedron WIP - perspective drawing on isometric dot paper

So I drew this dodecahedron and then the stellated dodecahedron below.

And when I drew that stellated dodecahedron I made some very annoying mistakes (in the last steps!)...

As I could not erase those ink lines, I improved and cut out the parts with mistakes...

Sadly, the cut outs are irritating for the perspective drawing. (I will show you why shading the faces will help make sense of this shape once I have made a second drawing of it.)

Now I cannot shade the stellated dodecehedron as it would look very messy with the cuts.

So I just use the stellated octahedron part as an interesting collage item.

I could even insert neon-colored paper, which would make it look fancy.

But for making a shaded drawing I might draw a second one - but without those mistakes...

[sharkrocket]

daniil crying daniil crying daniil crying

i like to imagine that he almost never cries and i just wanna know what finally makes him break down and ugly cry

OH MAN, I 100 percent agree with this, he strikes me as the kind of person to bottle up everything and try to push all his emotions down, but those emotions end up manifesting in negative/self-destructive ways until the weight of everything finally causes him to break down

There's a fic I love that does this really well, please read Shedding Skin by Plaguedboar, I binged all thirteen chapters in two days and was ugly crying by the end of it

Daniil and Artemy come to a slow harrowing realization about their feelings towards each other, but they both recognize how dangerous and destructive acting on those feelings might be. After Daniil takes a bullet for Artemy, it drives a wedge between them, Daniil pushing Artemy further and further away, as Artemy increasingly believes that Daniil sees him as something dangerous - something with the capacity to destroy him. That if Artemy allowed himself to love him and keep him in the town, Daniil will die

❗ SPOILERS ❗

The reason why Daniil ends up taking the bullet is because he realizes that he's also in love with Artemy, but truly believes that he's not worthy of being loved and that he'll ruin Artemy just like how he's ruined everything else he's touched. So, by dying by saving Artemy's life, it would have have been the best thing he could do for the both of them. However, because Artemy ends up saving him, Daniil becomes devastated and does everything in his power to make Artemy hate him and leave him, if he knows what's good for him. In turn, it causes Artemy to question if he's even capable of loving anyone. Thus, begins a cycle of Daniil being as cold and hateful as possible, throwing insults and being self-destructive, while Artemy keeps trying to save him, which only pushes Daniil to be more hateful and self-destructive....

❗ END SPOILERS ❗

There's a beautiful moment at the end where it culminates in Daniil walking out into the steppe to die, and against all odds, Artemy finds him there. After all this time, after all the insults, the coldness, the violence, Artemy decides to love Daniil despite it all and follows him into the wide expanse. Even then, the Capital Snake is still trying to spit venom - doing everything in his power to get Artemy to leave and let him die, but it doesn't work because Artemy finally sees through the facade. He reaches past the Bachelor's many roles and holds on to the Daniil that's terrified of loving and being loved in return, and that's when Daniil finally breaks and allows his vulnerability to bleed through

PLEASE READ THIS!! The angst and catharsis of it all is immense, and I can't recommend it enough!!

[notreallyherehahaha]

The Compound of the Cuboctahedron and Its Dual, the Rhombic Dodecahedron

Created with Stella 4d, which you can try for free here.

[a-alban-works]

[ketrinadrawsalot]

Polyhedron compounds are notoriously difficult to summon (the Stella Octangula is the simplest of these daemons). However, should the summoner succeed, they could answer unsolved mathematical problems. Assuming they don't go mad in the process of learning how...

[dailypolyhedra]

Polyhedron of the Day #100: Escher's solid

Escher's solid is a polyhedron, depicted in M.C. Escher's Waterfall. It has 48 faces, 72 edges, and 26 vertices. It is visually identical to the first stellation of the rhombic dodecahedron and the compound of three flattened octahedra. It can tessellate space to form a stellated rhombic dodecahedral honeycomb. A puzzle known as the Yoshimoto Cube is based on this fact. Its convex hull is a cuboctahedron.

[noosphe-re]

Tribe - A continuous set of semi-uniform polytopes (or compounds) that span several teepees. Truncation rotation is an example with one variable of morphing. Wythoffian cases will include all polytopes with a particular symbol (example xy^z) allowing the variables (x,y,z, etc) to take on any value including negative. The following pic displays the grid tribe (which contains 4 clans and 60 teepees). Each teepee is displayed twice on the pic with an example polyhedron within a triangle shaped region (the sides of the dual of grid). The grid tribe's clans are xy^z (grid), x,y^z (reboga), xy^'z (badori), and x,y^'z (robisu) - where x,y,and z take on positive values. There are 11 spitsu tribes under grid, they are xy^z (grid, 60 teepees), x*y^z (quitdid, 60 teepees), xy*z (gaquatid, 60 teepees), (x^y*'z) (idtid, 60 teepees), (xy*z) (becada, 30 teepees), (x^y^z,) (fabeca, 30 teepees), (xy^'z) (cafeta, 30 teepees), (x*y*z,) (mocaba, 30 teepees), (x^'y^'z^') (jefari, 10 teepees), (x*y*z*) (vamesa, 10 teepees), and the 15-block compound tribe x y z (broza, 5 teepees). I suspect that four dimensional tribes, such as the gidpixhi tribe could have as many as 7200 teepees with three variables of morphing. (source)

[azeez-unv]

Subject wise exhibition for schools of all the levels

AZEEZ

Some possible topics you can explore based on your interest and level of difficulty:

1. Science: You can choose from a variety of science projects that demonstrate the principles and phenomena of physics, chemistry, biology, astronomy, etc. For example, you can make a model of a solar system, a volcano, a DNA structure, a wind turbine, a water cycle, etc. You can also conduct experiments to test hypotheses and observe results. For example, you can test the effect of pH on plant growth, the effect of temperature on enzyme activity, the effect of light on photosynthesis, etc. You can find more science fair project ideas here.

2. Mathematics: You can showcase the beauty and applications of mathematics in everyday life by creating models, puzzles, games, patterns, etc. For example, you can make a model of a fractal, a tessellation, a polyhedron, a Mobius strip, etc. You can also design and solve problems that involve logic, geometry, algebra, calculus, etc. For example, you can create a Sudoku puzzle, a Rubik’s cube, a magic square, a Fibonacci spiral, etc. Principles of sequence and series in several spheres of human activities viz, calculating the amount of money over certain period of time under given rate of simple interest or compound interest/ finding depreciated or increased value of a certain commodity over a period of time Determining expenditures needed for manufacturing water tank / rectangular box/cylindrical/cone- shaped objects of a certain material provided cost of material per square/cube/unit are known; Determining perimeter, area of a region bounded by polygons/the circumference and area of a circular region/surface area and volume of cube/cuboid/cylinder/ cone/sphere/hemisphere of solid when two basic solids are joined together; Finding the ratio of area of quantities of substances in the formation of compounds or mixtures; Designs of parking area for maximum utilization of space; Predicting the population of species over certain period of time under given constraints; Applications of linear programming in solving problems pertaining to manufacturing of goods/transport/diet issues Applications of mathematics in decorating home e.g. how many rolls of wallpaper/number of tiles are needed to cover the wall; Using mathematics in cooking and nutrition/estimating number of calories and quantity of nutrients (carbohydrates, proteins, fats, minerals etc.) in a sample portion of various food items; Establishing a mathematical relation by considering all possible parameters to have maximum profit in producing certain items by a factory.

3. Environmental issues: The models and exhibits in this sub-theme may pertain to: Environmental issues related with human activities such as agriculture, energy, fishing, forests, mining, shipping, paper, war, ocean deoxygenation, dead zone, paint etc.; Environmental issues with energy conservation, renewable energy, efficient energy use, renewable energy commercialization etc; Environmental controversies such as dam controversies, genetically modified organisms/food controversy, sealing, dioxin controversy, water fluoridation controversy etc.; Environmental disasters such as the Bhopal disaster, oil spills, nuclear accidents etc. Climate change — global warming, greenhouse gases, fossil fuels, sea level rise, ocean acidification etc.; Issues related with environmental health such as air quality, asthma, electromagnetic radiations and fields, lead poisoning, indoor air quality, sick building syndrome etc; Water pollution — acid rain, marine pollution, Ocean dumping, eutrophication, marine debris, thermal pollution, algal boom, micro-plastics, etc; Air pollution — smog, ozone, particulate matter, sulphur oxide etc; Soil erosion, soil contamination and salination and Waste

4. Social Science: You can explore the various aspects of human society and culture by presenting topics related to history, geography, economics, politics, sociology, psychology, etc. For example, you can make a timeline of historical events, a map of different regions or countries, a poster of different currencies or flags, a chart of different forms of government or social systems, etc. You can also conduct surveys or interviews to collect data and analyze human behavior and opinions. For example, you can study the impact of social media on mental health, the factors that influence consumer choices, the effects of globalization on culture, etc.

5. Health: The exhibits and models in this sub-theme may pertain to: Demonstration of health and differentiation from the state of ill health; Sensitising people to be careful in health matters, explore the possibilities and make use of the facilities available; Development of knowledge-base and understanding new scientific, technological aids in bio- medical area; Demonstration of known facts and research findings in different medical systems like Indian, Modern, Homeopath etc.; Demonstration of lifestyle and relationship with good and bad health based on known facts and researches; Need for appropriate measures for family welfare; Need for developing low-cost nutritious food; General awareness about occupational hazards and innovative techniques to overcome them; General awareness about community medicine; Simple technologies for developing diagnostics and environmental monitoring.

6. Disaster management: The exhibits/ models in this sub-theme may pertain to: Better information and public address systems in the event of disaster to prevent chaos and confusion; Access of clean and safe drinking water in the event of disaster; Improvised/improved devices for effective communication between various emergency services-medical, police, military and other administrative bodies/committees; Various measures/models for planning, preparedness and coordination of different agencies in the even of disaster/community level preparedness for the various man-made disasters such as gas leakage, nuclear accidents, battery/bomb explosions, etc.; Use of geo-stationary satellites in providing information pertaining to meteorological processes; Technologies in forecasting and warning of cyclones, floods and storms; Innovative designs of flood alarm/flood forecasting and cyclone warning networks; Information management and early warning systems for flash floods; Studies of the impact of global warming on human health (spread of epidemic like dengue, malaria, yellow fever etc.; Designs and development of automatic weather recording devices etc..

7. Energy conversion: The exhibits/models in this sub-theme may pertain to: Models of green building/environment building which harvest energy, water and materials; Green roof technologies/roof mounted solar technologies such as solar water heater, solar lighting system; Models/innovative designs of domestic hydroelectric generator; Solar cooker/solar distiller/solar dryer for food processing/solar heated houses; Studies of variation in sunshine intensity at a given place for developing indigenous method of its usage etc; Projects for measuring availability of solar/wind energy in a given area; Use of tidal waves/ocean currents/salinity gradient for generating electricity; Energy from biomass such as seaweeds, human/animal wastes, keeping in view environmental concerns; Improvised technologies for effective usage of bio-fuels Innovative designs of bio gas/bio mass plant; Bio diesel from plant oils (obtained from canola, palm oil, micro algae oil, waste, vegetable oil etc); Low cost liquid fuel (bio-ethanol, bio methanol from cellulose biomass by improvising conversion techniques); Innovative designs of internal combustion engine which can function on various bio fuels; Production of electrical energy from mechanical energy/nuclear resources.

8. Agriculture and food safety: The exhibits/models in this sub-theme may pertain to: Studies of climatic change on agriculture; Managing crop yield due to climatic change arising from global warming; Preservation and conservation of soil and judicious use of water; Conventional biotechnology practices e.g., application of biotechnology, microbiology, genetic engineering and genomics to agriculture for improved and high yielding varieties; Organic farming/organic fertilisers versus chemical fertilisers; biodynamic liquid manure/green manure; Use of biotechnology for economically and ecologically sustainable biofuels; Environmental friendly measures of pest control; Application of biotechnology and genetic engineering in improving animal breeds and production of animal products that are used as food Innovative/inexpensive/improved/indigenous technologies/methods of storage/ preservation /conservation/transport of agricultural products and food materials Organic fertilizers versus chemical fertilizers; Food production and demand of quality food and food security; Nutrition education/healthy eating habits and food utilisation by body.

[stoportotouch]

air castle, on the other hand, is in 5/4

[knotty-et-al]

Compound of 3 rhombic dodecahedra

In motion:

[Rhombus module by Nick Robinson]

[sjweminem]

hi this might be the weirdest ask uve ever gotten but

https://newtonpermetersquare(.)tumblr(.)com/post/671754854936543232/weve-been-fooled

i like this meme but dont know enough math to properly ID it, and youre literally the only person on tumblr i can think to ask about math things...is there a special name for each of the the 3d functions? i think that polyhedron is a 5 cube compound????

answering wicked late cuz there's a massive pileup in my inbox (16 dead, 38 wounded) but oh this is FAR from my weirdest ask..

ok first of all let me just say i would suck a dick to get this on a shirt. but to answer your question (possibly) those first 2 graphs look a lot like the riemann zeta function. the third, with which i'm less familiar, looks like a twin dodecahedron? it's just another one of infinitely many polyhedra (if the name seems wild just know that the simple cube and pyramid, AKA a tetrahedron, are in that family- it basically just means "many sides" and the prefix states how many. my favorite is the octahedron!!!!). however idk if this graph is being used for any mathematical purpose beyond representing the shape three-dimensionally. that last graph is too small to figure out but my first instinct is to categorize it as a representation of a logarithmic spiral in 3D (once again if that label is unfamiliar, a much more well-known logarithmic function is the fibonacci sequence AKA the golden ratio). hopefully i'm wrong and it's something better cuz i fucking HATED logarithms in college

[notreallyherehahaha]

A Cube, Held Prisoner by a Stella Octangula

I made this three-part compound using Stella 4d (available here) to repeatedly tetstell a truncated octahedron.

[fellhellion]

it’s very interesting how Daniil frames each ending on day 12 in his quest log to be honest, his reasoning for picking each option. If you find out the nature of TPTB, it’s one of despair and he characterises himself as a hero who wanted to save lives but in the end is crushed by the fact that it’s all fictional. If u can’t invite Clara or Artemy, his decision is framed as both the idealistic reverence of what the Polyhedron represents and the compounding failure of his efforts to truly defeat the plague. Choosing Artemy’s decision is framed in Daniil’s mind as what the Hippocratic Oath demands he do in addition to being the choice best suited against a utopia that will crumble at the first sign of oppositon. And i didnt reload to see Clara’s but he notes that it would be like preserving a machine that forces the world into a state of limbo.

[materialsscienceandengineering]

Gold glue really does bond nanocages 'contradicting' logic

It has long been known that gold can be used to do things that philosophers have never even dreamed of. The Institute of Nuclear Physics of the Polish Academy of Sciences in Cracow has confirmed the existence of 'gold glue': bonds involving gold atoms, capable of permanently bonding protein rings. Skilfully used by an international team of scientists, the bonds have made it possible to construct molecular nanocages with a structure so far unparalleled in nature or even in mathematics.

The world of science has been interested in molecular cages for years. Not without reason. Chemical molecules, including those that would under normal conditions enter into chemical reactions, can be enclosed within their empty interiors. The particles of the enclosed compound, separated by the walls of the cage from the environment, have nothing to bond with. These cages can therefore be used, for example, to transport drugs safely into a cancer cell, only releasing the drug when they are inside it.

Molecular cages are polyhedra made up of smaller 'bricks', usually protein molecules. The bricks can't be of any shape. For example, if we wanted to build a molecular polyhedron using only objects with the outline of an equilateral triangle, geometry would limit us to only three solid figures: a tetrahedron, an octahedron or an icosahedron. So far, there have been no other structural possibilities.

Read more.

[dailypolyhedra]

Polyhedron of the Day #197: Compound of six decagrammic prisms

The compound of six decagrammic prisms is a uniform polyhedral compound. It has 72 faces (12 decagrams, 60 squares), 180 edges, and 120 vertices. It is also known as the great rhombisnub dodecahedron. Its Bowers-style acronym is grassid. Its component prisms are aligned with the axes of fivefold rotational symmetry of a dodecahedron. Its vertex figure is an isosceles triangle. Its dual is the compound of six decagrammic tegums.

Image created using Robert Webb's Stella software, found at http://www.software3d.com/Stella.php.

[phinnsyreads]

Item #: SCP-045

Object Class: Safe

Special Containment Procedures: SCP-045 is to be kept affixed to an examination platform in a hemispherical chamber measuring 5 meters in radius at Oceanographic Research Station 12, located at -██.██, -███.██ on the seafloor of the Pacific Ocean. The chamber is to be kept filled with gaseous neon at equilibrium pressure with the surrounding environment. The chamber is separated from habitable portions of the station by 5 meters of local seawater, and all interactions with SCP-045 are to be performed via telepresence or robotic means. The bindings that attach SCP-045 to its platform are fitted with quick-release latches, which are to be released when necessary to prevent a containment breach.

Given the seismic activity associated with SCP-045, if the containment chamber is damaged or breached by seismological activity, SCP-045 should be recovered by remotely controlled drone vehicles and kept at least 10 meters from human-inhabited spaces until such time as repairs can be completed to the optimal containment chamber.

Description: SCP-045 is an icosahedron composed of ice XII [a metastable form of water ice that is typically formed only within a narrow range of very high pressures and temperatures], heavily occluded with planar fractures in a regular, complex pattern. SCP-045 has an average radius of 1.7 meters and density of 2.6 g/cm³, which is approximately twice that of non-anomalous ice XII.

SCP-045 remains in a stable state at temperatures ranging from 0.074-500 kelvin (approx -273 ºC to 227 ºC) and pressures ranging from 0.4 pascals to 3 gigapascals (approx 3.95 microatmospheres to 29600 atmospheres). Although it is possible to melt or vaporize SCP-045 at temperatures and pressures outside of these ranges, the H2O involved is attracted to itself by unknown means and will remain within very close proximity unless forcibly separated. The water will refreeze as soon as conditions return to a position inside SCP-045's stable range and any subportions kept separate prior to refreezing will freeze into smaller icosahedrons identical in form and properties to the total amount of SCP-045.

Based on available evidence, it is currently believed that SCP-045 is a 3-dimensional projection of a hypericosahedron, a regular "polyhedron" that exists in 4 spatial dimensions and has 600 regular tetrahedral facets. Research is ongoing to determine how SCP-045 is able to maintain a stable lower-dimensional projection and whether this can be adapted for use when interacting with other dimensionally anomalous SCP Items.

At unpredictable intervals ranging from 2 weeks to 3 months, SCP-045 will spontaneously rotate around multiple axes simultaneously for a period no longer than 73 seconds. During this period, a series of small seismic events (<2.5 on the Richter scale) will occur in the immediate area of SCP-045. If SCP-045 is prevented from rotating, the seismic events increase in strength logarithmically to a maximum of 5.3 on the Richter scale. Following the end of the rotation period, the radius of SCP-045's effect will temporarily double for the same amount of time that it rotated.

When gaseous nitrogen or argon come within 3.7 meters of any portion of SCP-045, they are replaced by different compounds. N2 is replaced by liquid water at a conversion rate of 1.00 mol N2 : 1.98 mol H2O and Ar is replaced by crystalline NaCl ("table salt") at a conversion rate of 1.00 mol Ar : 4.26 mol NaCl. It should be noted that Nitrogen composes approximately 78% of the Earth's atmosphere by volume. Argon composes approximately 0.93% of the Earth's atmosphere by volume.

SCP-045 was discovered in 1972 when a Foundation submarine scouting the Pacific abyssal plain for suitable locations for undersea bases was diverted to investigate the epicenter of a series of unexpectedly localized, strong tremors. SCP-045 was found lodged in a crevice, which had apparently prevented it from rotating. When removed from the crevice, it was brought towards the vessel for further study and, upon coming within range of the interior atmosphere, exhibited its anomalous effects. This resulted in a catastrophic breach of internal containment protocols and the loss of 12 crew members prior to SCP-045 being released and the submarine moving out of range.

Addendum: Following several years of testing, it was accidentally discovered that SCP-045 also converts hydrogen gas into a random mixture of simple amino acids at a rate of 1 mol H2 : 0.04 mol amino acids. However, this conversion only occurs when the gas is diffused in saline water, such as that produced by SCP-045. Analysis of the seafloor surrounding the location where SCP-045 was discovered has revealed a large community of microfauna and microflora that is approximately 3 times as diverse as would be expected given the geology and location. All have biochemistry wherein the amino acids produced by SCP-045 are statistically overabundant, as compared to microbiota from similar geologic regions. Additionally, all thrive when immersed in pure saltwater devoid of other organic materials.

===

[Enjoy the podcast? Consider supporting us on Patreon! Patrons get access to bonus Joke episodes, outtakes, and can even request episodes on specific SCP objects.]