## New answers tagged polyhedra

2
votes

### Is there a pyramid with all four faces being right triangles?

Giving this StackExchange one last try.
In addition to the answer posted with triangular base, here is an example with a square base:
Use two 3-4-5 right triangles and two 3-5-sqrt(34) triangles.

3
votes

### Is there a pyramid with all four faces being right triangles?

If by pyramid, you mean the shape with a square base and four triangular sides, and you want the right angles all where the triangles meet, there is a solution, but it is degenerate.
Sample Vertices:
...

22
votes

### Is there a pyramid with all four faces being right triangles?

This picture of a quadrirectangular tetrahedron is from István Lénárt, `The Right Triangle as the Simplex in 2D Euclidean Space, Generalized to $n$ Dimensions'

Top 50 recent answers are included

#### Related Tags

polyhedra × 244mg.metric-geometry × 94

convex-polytopes × 87

discrete-geometry × 74

convex-geometry × 31

reference-request × 26

co.combinatorics × 19

gt.geometric-topology × 16

polytopes × 16

linear-programming × 13

computational-geometry × 13

graph-theory × 10

euclidean-geometry × 10

ag.algebraic-geometry × 9

at.algebraic-topology × 9

dg.differential-geometry × 8

tiling × 8

linear-algebra × 7

cones × 6

algorithms × 5

terminology × 5

plane-geometry × 5

simplicial-complexes × 5

ho.history-overview × 4

computational-complexity × 4