Snub cube calculator
Enter one edge length and get the volume and total surface of a snub cube: an edge of 1 gives a volume of about 7.889 and a surface of about 19.856. Left- and right-handed versions match. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Edge
- 1
- Volume
- 7.8894774
- Surface area
- 19.8564064606
- Formula surface area
- A = (6 + 8√3) a²
This calculator turns a single positive edge length into the two classic metrics of a snub cube, also known as the snub cuboctahedron: closed-form volume that depends on the tribonacci constant, and total surface area (6 + 8√3) times edge squared.
What a snub cube calculator returns and why edge length is enough
A snub cube is one of the thirteen Archimedean solids: thirty-two equilateral triangular faces, six square faces, twenty-four vertices where five triangles and one square meet in an alternating chiral pattern, and sixty equal edges. Because every face is regular and every vertex figure is the same up to mirror image, a single positive edge length a completely determines the solid up to rigid motion and chirality. Left-handed and right-handed snubs share the same volume and surface area, so this tool does not need a handedness flag.
It exists to turn that one length into a deterministic response without forcing you to look up the tribonacci constant, which radical multiplies by a cubed for volume, or whether surface area means one face or the whole net of thirty-eight polygons. If you need a regular cube, dodecahedron, or icosahedron only, use the dedicated Platonic tools; the search intent here is the snub cube from edge length and a clear answer or an honest error when the edge is not positive.
How the closed forms are evaluated: volume, surface, and the tribonacci constant
Surface area multiplies six plus eight times the square root of three by edge squared: six square faces contribute six a squared, and thirty-two equilateral triangles contribute thirty-two times square root of three over four times a squared, which simplifies to eight square root of three times a squared, for a compact total of open parenthesis six plus eight square root of three close parenthesis a squared.
Volume uses the Wikipedia-standard expression with the tribonacci constant t, the unique real root of x cubed minus x squared minus x minus one equals zero, evaluated in closed form as one plus the cube root of nineteen plus three square root of thirty-three plus the cube root of nineteen minus three square root of thirty-three, all over three. Volume is then open parenthesis eight t plus six close parenthesis over three times the square root of two times open parenthesis t squared minus three close parenthesis, times edge cubed.
Optional precision only rounds the published fields; the internal solve always uses full double precision before that final rounding step.
What you can do with it
Homework and Archimedean-solid drills
Compute snub cube volume and total surface from textbook edge length, and verify that negative or non-positive edges are rejected.
3D models, packaging, and game assets
Size snub-cubic containers, print nets, or procedural chiral meshes from a known edge in CAD, manufacturing, and simulation tools.
FAQ
What does the snub cube calculator cost?
It is free in your browser on this page.
Which formulas are used?
Surface area is A = (6 + 8√3) a². Volume is V = (8t + 6) / (3 √(2(t² − 3))) a³ where t is the tribonacci constant, the real root of x³ − x² − x − 1 = 0.
How many faces, edges and corners does a snub cube have?
It has thirty-eight faces, thirty-two equilateral triangles and 6 squares, plus 60 equal edges and 24 corners where five triangles and one square meet.
Do left-handed and right-handed snub cubes give different results?
No. The two mirror-image versions share the same volume and surface area, so you only enter the edge length and never choose a handedness.
Why does the volume use the tribonacci constant?
The exact volume of the snub cube is built on that number, the real root of t cubed minus t squared minus t minus one. The calculator works it out for you, so there is nothing to look up.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/geom/snub-cube \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"edge":1}'const res = await fetch("https://api.kit.forhosting.com/geom/snub-cube", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"edge": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geom/snub-cube",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"edge": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/snub-cube", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"edge":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"edge":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/snub-cube", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"edge": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geom.snub_cube",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
You enter the edge as a finite positive length; the engine returns edge, volume, surface_area, and formula strings so a student or a log line can verify the identity without reading the source. When the edge is missing, zero, negative, or non-finite, the tool returns invalid_input instead of a silent NaN. Through the API a successful request costs $0.002; validation failures are not charged.
What a snub cube calculator returns and why edge length is enough
The response always echoes edge, reports volume from the standard Archimedean closed form involving the tribonacci constant t, surface_area as the total of all thirty-eight faces, and formula strings for both so a student or a log line can verify the identity without reading the source. Missing edge, non-finite values, zero length, or a negative edge all raise invalid_input with a message that names the failing field and states that the edge must be positive. That discipline keeps automated tests stable, makes caching safe, and prevents a script from treating a degenerate segment as a real solid.
How the closed forms are evaluated: volume, surface, and the tribonacci constant
The engine resolves edge from the field edge with aliases a, edge_length, and side, requiring the value to be finite and strictly greater than zero so that negative edge is always rejected. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the tribonacci radicals yourself.
Where snub cube metrics fit in study, design, and code
Students meet the snub cube when a textbook asks for Archimedean volume from edge length, when an exam demands total surface of a chiral solid, or when solid-geometry homework wants material estimates for a thirty-eight-faced model before painting or 3D printing. Teachers can pre-generate answer keys that list volume and surface for integer edges, and that refuse zero or negative lengths instead of printing NaN. Mechanical and product design sometimes needs the capacity of a snub-cubic container, the sheet area of a folded net, or a sanity check against a CAD volume property; knowing that a requested edge is not positive is as valuable as the number itself. Game and simulation teams use volume and surface for collision approximations, particle bounds, and procedural mesh sizing that should stay deterministic across platforms, including left and right enantiomorphs that share the same scalar metrics. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split—free interactive exploration and a priced, identical API—matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with other free geometry endpoints when you need cube, dodecahedron, or icosahedron solvers for a lab of deterministic tools, and with documentation that shows both the edge and the finished metrics so the numbers and the picture stay aligned for learners and reviewers. Whether you arrived searching for a snub cube calculator or for snub cuboctahedron volume and surface from edge length, the contract is the same: positive edge in, finite metrics or a clear invalid_input out when the edge is negative or otherwise invalid.
Integration use cases
Deterministic geometry fixtures
Generate reproducible snub cube metrics for unit tests, contest validators, and CI assertions without hand-rolled tribonacci coefficients.
Technical questions
What if the edge length is negative or zero?
The handler returns invalid_input with a message that the edge must be a positive finite number; negative edge is not accepted.
Does surface_area mean one face or the whole solid?
surface_area is the total surface of all thirty-eight faces (thirty-two equilateral triangles and six squares). It is not a single face area.
Can I control rounding?
Yes. Set precision (aliases decimals, dp) to an integer from 0 to 15; the default is 10 decimal places on all numeric fields.