Cubic pyramid (EntityTopic, 23)

(Redirected from Rotope 15)

The cubic pyramid is a CRF polychoron among Klitzing's list of segmentochora (K4.26). It is bounded by its cubical base and 6 square pyramidal sides.

Dichoral angles

• Between cube and square pyramid: 45° (exact)
• Between two adjacent square pyramids: 180° - acos(1/3) ≈ 109.4712206345°

Equations

• Variables:
l ⇒ length of edges of the cubic pyramid
total edge length = 20l
total surface area = (6 + 3√3) · l2
surcell volume = (1 + √2) · l3
bulk = 18 · l4
[!x,!y,!z] ⇒ square pyramid
[!w] ⇒ cube

Net

The net of a cubic pyramid is a cube surrounded by six square pyramids.

Coordinates

The coordinates of a cubic pyramid with side 2 are:

(±1, ±1, ±1, 0)
(0, 0, 0, 1)

Incidence matrix

Dual: octahedral pyramid

 # TXID Type Name Va Vb Ea Eb 3a 4a C1a C2a 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 = square ; lateral: faces 6 C1a 1 4 4 4 4 1 = square pyramid ; sweep: faces 7 C2a 0 8 0 12 0 6 = base of pyramid: cube ; lateral: cell 8 H4.1a 1 8 8 12 12 6 6 1 = cubic pyramid ;

Usage as facets

This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.

 Notable Tetrashapes Regular: pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron Powertopes: triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate Circular: glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder Torii: tiger • torisphere • spheritorus • torinder • ditorus

 18. [21]1Cylindrone 19. [111]1Cubic pyramid 20. 211Cyltrianglinder List of tapertopes