Square pyramid (EntityTopic, 23)
From Hi.gher. Space
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| dim=3 | | dim=3 | ||
| elements=5, 8, 5 | | elements=5, 8, 5 | ||
| + | | sym=[[Stauroaxial symmetry|C<sub>4v</sub>]] | ||
| genus=0 | | genus=0 | ||
| ssc=G4P | | ssc=G4P | ||
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| flayout={{FLD|a4|i|ade|cr|e4}} | | flayout={{FLD|a4|i|ade|cr|e4}} | ||
| dual=''Self-dual'' | | dual=''Self-dual'' | ||
| + | | bowers=Squippy | ||
}}}} | }}}} | ||
A '''square pyramid''' is a special case of a [[pyramid]] where the base is a [[square]]. | A '''square pyramid''' is a special case of a [[pyramid]] where the base is a [[square]]. | ||
Revision as of 22:08, 2 March 2014
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
- The hypervolumes of a square pyramid are given by:
total edge length = 8l
surface area = (1 + √3) · l2
volume = √2∕6 · l3
- The planar cross-sections (n) of a square pyramid are:
[!x,!y] ⇒ triangle
[!z] ⇒ square
Incidence matrix
Dual: Self-dual
| # | TXID | Va | Vb | Ea | Eb | 3a | 4a | Type | Name |
|---|---|---|---|---|---|---|---|---|---|
| 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
- 12× 1-facets of a cubic bipyramid
- 6× 1-facets of a cubic pyramid (named sweep: faces)
- 2× 1-facets of a square pyramid bipyramid
- prism: 2× 1-facets of a square pyramid prism
- 4× 1-facets of a gyrated octahedral prism
- 4× 1-facets of a K4.13 dual
- 4× 1-facets of a K4.8
- 4× 1-facets of a K4.8 dual
- 8× 1-facets of a (dual of square biantiprismatic ring)
- 4× 1-facets of a square biantiprismatic ring
- 288× 1-facets of a (dual of truncated snub demitesseract)
- 8× 1-facets of a (dual of bilunabirotunda pseudopyramid)
- 4× 1-facets of a bilunabirotunda pseudopyramid
- 3× 1-facets of a D4.16
- 120× 1-facets of a D4.3.2 dual
- 240× 1-facets of a D4.3.2 dual
- 8× 1-facets of a (dual of bitrigonal diminished pyrocantichoron)
- 8× 1-facets of a (dual of bitrigonal diminished pyrocantichoron)
- 4× 1-facets of a bitrigonal diminished pyrocantichoron
- 8× 1-facets of a (4D analog of J37)
- 16× 1-facets of a (4D analog of J37)
- 6× 1-facets of a (dual of triangular hebesphenorotunda pseudopyramid)
- 3× 1-facets of a (dual of triangular hebesphenorotunda pseudopyramid)
- 6× 1-facets of a (dual of triangular hebesphenorotunda pseudopyramid)
- 3× 1-facets of a triangular hebesphenorotunda pseudopyramid (named tola to roof)
- 12× 1-facets of a triangular hebesphenorotundaeic rhombochoron (named oobpp)
- 12× 1-facets of a triangular hebesphenorotundaeic rhombochoron (named ooggb)
- 6× 1-facets of a triangular hebesphenorotundaeic rhombochoron (named roooo)
- 6× 1-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron (named roooo)
- 12× 1-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron (named ooggb)
- 12× 1-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron (named oobpp)
- 12× 1-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron (named tola to roof)
- 6× 1-facets of a D4.7
- 24× 1-facets of a D4.7 dual
- 24× 1-facets of a D4.7 dual
| 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. 21 Cone | 9. [11]1 Square pyramid | 10. 111 Triangular prism |
| List of tapertopes | ||
