spring-of-mathematics:

A pyritohedron is a dodecahedron with pyritohedral (Th) symmetry. Like the regular dodecahedron, it has twelve identical pentagonal faces, with three meeting in each of the 20 vertices. However, the pentagons are not necessarily regular, so the structure normally has no fivefold symmetry axes. Its 30 edges are divided into two sets - containing 24 and 6 edges of the same length.

Although regular dodecahedra do not exist in crystals, the distorted, pyritohedron form occurs in the crystal pyrite, and it may be an inspiration for the discovery of the regular Platonic solid form.

The pyritohedron has a geometric degree of freedom with limiting cases of a cubic convex hull at one limit of colinear edges, and a rhombic dodecahedron as the other limit as 6 edges are degenerated to length zero. The regular dodecahedron represents a special intermediate case where all edges and angles are equa - Image:

  1. A cube can be divided into a pyritohedron by bisecting all the edges, and faces in alternate directions (2 : 1) & h= 0.
  2. Regular star, great stellated dodecahedron, with pentagonal distorted into regular pentagrams (1 : 1)
  3. Concave pyritohedral dodecahedron (1 : 1).
  4. The geometric proportions of the pyritohedron in the Weaire–Phelan structure (1.3092… : 1)
  5. A regular dodecahedron is an intermediate case with equal edge lengths (1 : 1) & h=(√5−1)/2.
  6. A rhombic dodecahedron is the limiting case with the 6 crossedges reducing to length zero (0 : 1) & h=0.

Cartesian coordinates: The coordinates of the 8 vertices of the original cube are: (±1, ±1, ±1)
The coordinates of the 12 vertices of the cross-edges are:
 (0, ±(1+h), ±(1−h^2))
 (±(1+h), ±(1−h^2), 0)
 (±(1−h^2), 0, ±(1+h))
where h is the height of the wedge-shaped “roof” above the faces of the cube. When h=1, the six cross-edges degenerate to points and a rhombic dodecahedron is formed. When h=0, the cross-edges are absorbed in the facets of the cube, and the pyritohedron reduces to a cube. When h=(√5−1)/2, the inverse of the golden ratio, the original edges of the cube are absorbed in the facets of the wedges, which become co-planar, resulting in a regular dodecahedron.

Image & the article : Shared at http://en.wikipedia.org/wiki/Dodecahedron & Dodécaèdre on Wikipedia.

thisiseverydayracism:

As darkness fell on Canfield Drive on August 9, a makeshift memorial sprang up in the middle of the street where Michael Brown’s body had been sprawled in plain view for more than four hours. Flowers and candles were scattered over the bloodstains on the pavement. Someone had affixed a stuffed animal to a streetlight pole a few yards away. Neighborhood residents and others were gathering, many of them upset and angry.

Soon, police vehicles reappeared, including from the St. Louis County Police Department, which had taken control of the investigation. Several officers emerged with dogs. What happened next, according to several sources, was emblematic of what has inflamed the city of Ferguson, Missouri, ever since the unarmed 18-year-old was gunned down: An officer on the street let the dog he was controlling urinate on the memorial site.

The incident was related to me separately by three state and local officials who worked with the community in the immediate aftermath of the shooting. One confirmed that he interviewed an eyewitness, a young woman, and pressed her on what exactly she saw. “She said that the officer just let the dog pee on it,” that official told me. “She was very distraught about it.” The identity of the officer who handled the dog and the agency he was with remain unclear.

Candles and flowers marking the spot where Brown died were soon run over by police vehicles.

The day brought other indignities for Brown’s family, and the community. Missouri state Rep. Sharon Pace, whose district includes the neighborhood where the shooting occurred, told me she went to the scene that afternoon to comfort the parents, who were blocked by police from approaching their son’s body. Pace purchased some tea lights for the family, and around 7 p.m. she joined Brown’s mother, Lesley McSpadden, and others as they placed the candles and sprinkled flowers on the ground where Brown had died. “They spelled out his initials with rose petals over the bloodstains,” Pace recalled.

By then, police had prohibited all vehicles from entering Canfield Drive except for their own. Soon the candles and flowers had been smashed, after police drove over them.

"That made people in the crowd mad," Pace said, "and it made me mad." Some residents began walking in front of police vehicles at the end of the block to prevent them from driving in.

More: http://m.motherjones.com/politics/2014/08/ferguson-st-louis-police-tactics-dogs-michael-brown

thisiseverydayracism:

As darkness fell on Canfield Drive on August 9, a makeshift memorial sprang up in the middle of the street where Michael Brown’s body had been sprawled in plain view for more than four hours. Flowers and candles were scattered over the bloodstains on the pavement. Someone had affixed a stuffed animal to a streetlight pole a few yards away. Neighborhood residents and others were gathering, many of them upset and angry.

Soon, police vehicles reappeared, including from the St. Louis County Police Department, which had taken control of the investigation. Several officers emerged with dogs. What happened next, according to several sources, was emblematic of what has inflamed the city of Ferguson, Missouri, ever since the unarmed 18-year-old was gunned down: An officer on the street let the dog he was controlling urinate on the memorial site.

The incident was related to me separately by three state and local officials who worked with the community in the immediate aftermath of the shooting. One confirmed that he interviewed an eyewitness, a young woman, and pressed her on what exactly she saw. “She said that the officer just let the dog pee on it,” that official told me. “She was very distraught about it.” The identity of the officer who handled the dog and the agency he was with remain unclear.

Candles and flowers marking the spot where Brown died were soon run over by police vehicles.

The day brought other indignities for Brown’s family, and the community. Missouri state Rep. Sharon Pace, whose district includes the neighborhood where the shooting occurred, told me she went to the scene that afternoon to comfort the parents, who were blocked by police from approaching their son’s body. Pace purchased some tea lights for the family, and around 7 p.m. she joined Brown’s mother, Lesley McSpadden, and others as they placed the candles and sprinkled flowers on the ground where Brown had died. “They spelled out his initials with rose petals over the bloodstains,” Pace recalled.

By then, police had prohibited all vehicles from entering Canfield Drive except for their own. Soon the candles and flowers had been smashed, after police drove over them.

"That made people in the crowd mad," Pace said, "and it made me mad." Some residents began walking in front of police vehicles at the end of the block to prevent them from driving in.

More: http://m.motherjones.com/politics/2014/08/ferguson-st-louis-police-tactics-dogs-michael-brown

majiinboo:

  • Do not forget Michael Brown
  • Do not forget how the media dehumanized him and tried to justify his murder
  • Do not forget how peaceful protests were painted as savage riots
  • Do not forget police armed with military grade weapons terrorized and arrested black civilians
  • Do not forget Darren Wilson being awarded over $200,000 in fundraiser donations for murdering an unarmed black child
  • Do not forget that this system was not built to defend us, but to control us
  • Do not forget Ferguson 
strugglingtobeheard:

atriptothemorg:

fuckyeahmarxismleninism:

Six Facts About Harriet Tubman
1. Harriet Tubman’s birth name was Aramita (“Minty”) Ross. She was born enslaved in Maryland sometime in 1820.
2. Tubman escaped slavery with her brother, Ben and Harry, on September 17, 1849.

3. Tubman is most famous for her role as a conductor on the Underground Railroad, in which she led escaped slaves to freedom. Estimates vary, but Tubman is said to have helped anywhere from dozens to hundreds of slaves reach freedom. She was once quoted as saying, “I freed a thousand slaves. I could have freed a thousand more if only they knew they were slaves.”
4. During the Civil War, Tubman worked for the Union army as a cook, nurse, and spy. She was also the first woman to lead an expedition in the war and guided the Combahee River Raid, which freed 700 slaves. Decades later, the raid would inspire a groundbreaking group of black feminists called the Combahee River Collective.
5. Tubman’s life has inspired countless works for art, including poems, comic books, and films.
6. This year marks that 100th anniversary of Harriet Tubman’s death. Maryland has a series of commemorative events. 

The last one really hits me. She had only been dead for 100 years. 100 years. Like, white folks are going on and on about how slavery has been over for hundreds and hundreds of years.
But here is an escaped slave who liberated countless others that only died ONE HUNDRED YEARS ago. This is not the ancient past. This is still living history.

^^^^^^^^^^^^^^^^^^^^^^

strugglingtobeheard:

atriptothemorg:

fuckyeahmarxismleninism:

Six Facts About Harriet Tubman

1. Harriet Tubman’s birth name was Aramita (“Minty”) Ross. She was born enslaved in Maryland sometime in 1820.

2. Tubman escaped slavery with her brother, Ben and Harry, on September 17, 1849.

Harriet_Tubman_Reward_Notice_1849.jpg

3. Tubman is most famous for her role as a conductor on the Underground Railroad, in which she led escaped slaves to freedom. Estimates vary, but Tubman is said to have helped anywhere from dozens to hundreds of slaves reach freedom. She was once quoted as saying, “I freed a thousand slaves. I could have freed a thousand more if only they knew they were slaves.”

4. During the Civil War, Tubman worked for the Union army as a cook, nurse, and spy. She was also the first woman to lead an expedition in the war and guided the Combahee River Raid, which freed 700 slaves. Decades later, the raid would inspire a groundbreaking group of black feminists called the Combahee River Collective.

5. Tubman’s life has inspired countless works for art, including poemscomic books, and films.

6. This year marks that 100th anniversary of Harriet Tubman’s death. Maryland has a series of commemorative events

The last one really hits me. She had only been dead for 100 years. 100 years. Like, white folks are going on and on about how slavery has been over for hundreds and hundreds of years.

But here is an escaped slave who liberated countless others that only died ONE HUNDRED YEARS ago. This is not the ancient past. This is still living history.

^^^^^^^^^^^^^^^^^^^^^^

(via afro-caribbeansistah)