q2K BHP
Black History Portal
THE BHP WIRE —
HIDDEN TRUTHS
What's New!
THE JOURNEY THROUGH TIME

Explore Black History

Explore the people, places, events, achievements, struggles and stories that shaped our journey.

✊🏾

Civil Rights

Movements, leaders, victories and the continuing fight for equality.

⚙️

Black Inventors

Innovation, patents, science, technology and world-changing contributions.

🏆

Sports

Pioneers, champions, Negro Leagues, records, activism and excellence.

♟️

People

Meet the people whose lives, choices and achievements shaped the journey.

📍

Places

Black towns, communities, institutions and places where history happened.

📜

Events

Moments that changed communities, movements, institutions and the nation.

Enter a person, place, event, or topic.
MY'STORY

The MOVE Fire

This is a personal recollection on the Move fire on May 13, 1985 Philadelphia police fired thousands of rounds at the MOVE house, city officials approved dropping an explosive device on the roof, the resulting fire was allowed to burn, 11 people—including five children—died, and 61 homes were destroyed. Philadelphia City Council later called it a “brutal attack carried out by the City of Philadelphia on its own citizens” and acknowledged that no individual faced criminal consequences for the bombing. One timeline correction worth preserving for the BHP record: the major previous MOVE-police confrontation was August 8, 1978, about seven years before the bombing, not a year or two earlier. Officer James Ramp was killed, other police and firefighters were wounded, nine MOVE members were later convicted, and television cameras recorded police beating Delbert Africa during his arrest. The 1985 MOVE Commission later specifically criticized city planners for failing to adequately use lessons from that 1978 confrontation. And that actually strengthens the point you’re making: 1985 did not happen without precedent or institutional memory. There had already been a deadly confrontation with MOVE, years of conflict, negotiations and police involvement before Osage Avenue.

MORE →
BLACK FACTS
The Truths They Never Taught You...

Ruler of the Mali Empire in the 14th century

Mansa Musa was the ruler of the Mali Empire in West Africa. Details recorded here should be sourced; unknown information is left blank.

MORE →
BHP gathered finds from its connected research sources. Showing the 4 strongest Black History matches.
← BACK TO RESULTS
Wikipedia

Heptagonal tiling

Heptagonal tiling
Heptagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration 73
Schläfli symbol {7,3}
Wythoff symbol 3 | 7 2
Coxeter diagram
Symmetry group [7,3], (*732)
Dual Order-7 triangular tiling
Properties Vertex-transitive, edge-transitive, face-transitive

In geometry, the heptagonal tiling is a regular tiling of the hyperbolic plane. It is represented by Schläfli symbol of {7,3}, having three regular heptagons around each vertex.

Images

[edit]

Poincaré half-plane model

Poincaré disk model

Beltrami-Klein model
[edit]

This tiling is topologically related as a part of sequence of regular polyhedra with Schläfli symbol {n,3}.

*n32 symmetry mutation of regular tilings: {n,3}
Spherical Euclidean Compact hyperb. Paraco. Noncompact hyperbolic
{2,3} {3,3} {4,3} {5,3} {6,3} {7,3} {8,3} {∞,3} {12i,3} {9i,3} {6i,3} {3i,3}

From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular heptagonal tiling.

Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms.

Uniform heptagonal/triangular tilings
Symmetry: [7,3], (*732) [7,3]+, (732)
{7,3} t{7,3} r{7,3} t{3,7} {3,7} rr{7,3} tr{7,3} sr{7,3}
Uniform duals
V73 V3.14.14 V3.7.3.7 V6.6.7 V37 V3.4.7.4 V4.6.14 V3.3.3.3.7

Hurwitz surfaces

[edit]
The symmetry group of the heptagonal tiling has fundamental domain the (2,3,7) Schwarz triangle, which yields this tiling.

The symmetry group of the tiling is the (2,3,7) triangle group, and a fundamental domain for this action is the (2,3,7) Schwarz triangle. This is the smallest hyperbolic Schwarz triangle, and thus, by the proof of Hurwitz's automorphisms theorem, the tiling is the universal tiling that covers all Hurwitz surfaces (the Riemann surfaces with maximal symmetry group), giving them a tiling by heptagons whose symmetry group equals their automorphism group as Riemann surfaces. The smallest Hurwitz surface is the Klein quartic (genus 3, automorphism group of order 168), and the induced tiling has 24 heptagons, meeting at 56 vertices.

The dual order-7 triangular tiling has the same symmetry group, and thus yields triangulations of Hurwitz surfaces.

See also

[edit]

References

[edit]
  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
  • "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.
[edit]

Source: Wikipedia. Article content is retrieved live through the MediaWiki API.

Wikipedia

Heptagonal tiling

In geometry, the heptagonal tiling is a regular tiling of the hyperbolic plane. It is represented by Schläfli symbol of {7,3}, having three regular heptagons around each vertex.

MORE →
Wikipedia

Truncated heptagonal tiling

In geometry, the truncated heptagonal tiling is a semiregular tiling of the hyperbolic plane. There are one triangle and two tetradecagons on each vertex. It has Schläfli symbol of t{7,3}. The tiling has a vertex configuration of 3.14.14.

MORE →
Wikipedia

Order-4 heptagonal tiling

In geometry, the order-4 heptagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {7,4}.

MORE →
Wikipedia

Truncated order-4 heptagonal tiling

In geometry, the truncated order-4 heptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{7,4}.

MORE →
TOPIC OF THE DAY

Greenwood / Black Wall Street

Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.

MORE →
TRIVIA QUESTION OF THE DAY

Who was the first African-American woman millionaire in the United States?

Madam C.J. Walker