# Square pyramid (EntityTopic, 23)

A square pyramid is a special case of a pyramid where the base is a square.

## Equations

• Variables:
l ⇒ length of edges of the square pyramid
total edge length = 8l
surface area = (1 + √3) · l2
volume = √26 · l3
[!x,!y] ⇒ triangle
[!z] ⇒ square

## Incidence matrix

Dual: Self-dual

 # TXID Type Name Va Vb Ea Eb 3a 4a 0 Va = point ; sweep: apex 1 Vb = point ; lateral: vertices 2 Ea 1 1 = digon ; sweep: vertices 3 Eb 0 2 = digon ; lateral: edges 4 3a 1 2 2 1 = triangle ; sweep: edges 5 4a 0 4 0 4 = base of pyramid: square ; lateral: faces 6 C1a 1 4 4 4 4 1 = square pyramid ;

## Usage as facets

 Notable Trishapes Regular: tetrahedron • cube • octahedron • dodecahedron • icosahedron Direct truncates: tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate Mesotruncates: stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron Snubs: snub staurohedron • snub rhodohedron Curved: sphere • torus • cylinder • cone • frustum • crind

 8. 21Cone 9. [11]1Square pyramid 10. 111Triangular prism List of tapertopes