Cubic pyramid (EntityTopic, 23)

From Higher Dimensions Database

The cubic pyramid is a CRF polychoron among Klitzing's list of segmentochora (K4.26).

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 = 14 · l4
[!x,!y,!z] ⇒ triangle
[!w] ⇒ square

Net

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

Coordinates

apacs<1,1,1> ~ <0>
<0,0,0,1>

Incidence matrix

Dual: octahedral pyramid

#TXIDVaVbEaEb3a4aC1aC2aTypeName
0 Va = point ; sweep: apex
1 Vb = point ; lateral: vertices
2 Ea 11 = digon ; sweep: vertices
3 Eb 02 = digon ; lateral: edges
4 3a 1221 = triangle ; sweep: edges
5 4a 0404 = square ; lateral: faces
6 C1a 144441 = square pyramid ; sweep: faces
7 C2a 0801206 = base of pyramid: cube ; lateral: cell
8 H4.1a 1881212661 = cubic pyramid ;

Usage as facets

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


Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonediconeconinder
Torii: tigertorispherespheritorustorinderditorus


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