Snub dodecahedron calculator
Enter one edge length and get the size of a snub dodecahedron: an edge of 1 gives a volume of about 37.6167 and a surface of about 55.2867, spread over 92 faces. Both mirror-image forms 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
- 37.6166499627
- Surface area
- 55.2867449584
- Faces
- 92
- Edges
- 150
A snub dodecahedron is the chiral Archimedean solid obtained by snubifying a regular dodecahedron or icosahedron so that every original face becomes a regular polygon and the gaps fill with equilateral triangles twisted in a consistent handedness. Students, 3D designers, and exam writers need its volume and total surface area from a single shared edge length when sizing near-spherical shells, checking textbook Archimedean tables, or scripting parametric models.
What a snub dodecahedron is and which formulas fix volume and surface
Start from a regular dodecahedron or icosahedron and apply snubification: expand and twist the faces so that every original edge is replaced by two equilateral triangles and every original face shrinks to a regular polygon of the same type. The resulting convex polyhedron is the snub dodecahedron, one of the thirteen Archimedean solids and the only Archimedean solid with ninety-two faces. It has eighty equilateral triangular faces and twelve regular pentagonal faces, one hundred fifty equal edges, and sixty identical vertices.
Because snubification introduces a preferred twist direction, the solid exists in two enantiomorphic forms (laevo and dextro) that are mirror images of each other; both share the same edge length, volume, and surface area. A single non-negative length a completely determines the metrics up to congruence.
The surface area is elementary: eighty equilateral triangles of side a plus twelve regular pentagons of side a yield S equals twenty times the square root of three plus three times the square root of twenty-five plus ten times the square root of five, times a squared. When a is zero the solid collapses and both volume and surface area are zero; when a is positive both grow as a cubed and a squared respectively.
Negative a has no interpretation as a geometric edge length, so this capability refuses it rather than taking an absolute value that would hide a data-entry bug.
Where the snub dodecahedron figures help
Classrooms and tutoring platforms use a snub dodecahedron calculator so learners can check volume and surface area for arbitrary non-negative edge lengths without mixing the eighty-triangle and twelve-pentagon face formulas by hand or solving the snub cubic themselves. Exam-prep generators need a deterministic oracle that marks negative edges as invalid input instead of silently reflecting the absolute value or inventing a positive volume. Failed validation does not consume balance.
Compared with a plain dodecahedron or icosidodecahedron calculator, this landing targets the narrower search intent of the snub dodecahedron alone, so SEO pages do not compete for ordinary Platonic or rectified solid volume queries while still serving the exact scalars designers and students ask for when they type snub dodecahedron into a search box and need volume plus surface area from edge length.
What you can do with it
Classroom checks of snub dodecahedron metrics
Let students submit an edge length and verify volume involving φ and ξ against textbook Archimedean tables, plus surface S=(20√3+3√(25+10√5))·a² from eighty triangles and twelve pentagons.
CAD and parametric design notebooks
Compute volume and surface area for snub dodecahedron cells in scripts that size decorative chiral polyhedra, high-sphericity shells, or clearance envelopes.
Exam generators and LMS auto-grading
Mark solid-geometry items with a deterministic oracle that rejects negative edges and pins twelve-decimal goldens for volume and surface area.
FAQ
Which formulas does the calculator use?
Surface area S = (20√3 + 3√(25+10√5)) · a².
What happens if the edge is negative?
A snub dodecahedron requires a non-negative edge length; negative values are rejected and those calls are not charged.
Is the snub dodecahedron calculator free?
The browser tool runs free on your device.
How does a snub dodecahedron differ from a dodecahedron or icosidodecahedron?
A regular dodecahedron has twelve pentagons only. An icosidodecahedron has twenty triangles and twelve pentagons (rectified). A snub dodecahedron has eighty equilateral triangles and twelve regular pentagons (92 faces, 150 edges, 60 vertices) and is chiral.
What happens to the volume and surface when the edge doubles?
The volume grows eight times and the surface four times, because volume depends on the edge cubed and surface on the edge squared. An edge of 2 therefore gives about eight times 37.6167.
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-dodecahedron \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"edge":1}'const res = await fetch("https://api.kit.forhosting.com/geom/snub-dodecahedron", {
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-dodecahedron",
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-dodecahedron", 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-dodecahedron", 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_dodecahedron",
"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
Negative edges are rejected with invalid_input so automation never treats a sign error as a physical solid. The free browser path and the paid API path share the same pure module, so classroom checks and production pipelines always agree on twelve-decimal rounding. At $0.002 per successful API call there is no model spend and no outbound network—only analytic arithmetic on one finite scalar.
What a snub dodecahedron is and which formulas fix volume and surface
Reporting volume, surface_area, and the topology triple faces, edges, vertices matches textbook language and CAD notebooks without forcing clients to re-derive face counts from memory.
Input contract, response shape, and error behaviour
Example: edge equals one yields volume approximately thirty-seven point six one seven and surface area approximately fifty-five point two eight seven in consistent cubic and square units. Edge equals two scales volume by eight and surface area by four because of the a cubed and a squared dependence. Keep requests small, pin the rounded volume and surface area in automated tests, and you get reproducible Archimedean metrics for homework, LMS plugins, and edge workers without standing up a full solid-geometry library. POST a JSON body with one required field edge: a finite number or numeric string for the common edge length of the snub dodecahedron. Aliases a, side, edge_length, and length are accepted and mapped to the same parameter so notebook cells and form widgets can keep their local naming. Missing, empty, or non-finite values fail with invalid_input naming the field. On success the body echoes edge rounded to twelve decimal places, volume, surface_area, faces set to ninety-two, edges set to one hundred fifty, vertices set to sixty, method set to snub_dodecahedron, and two formula strings for display next to the answer: the volume expression in terms of φ and ξ, and S equals open parenthesis twenty square root of three plus three square root of twenty-five plus ten square root of five close parenthesis times a squared. Pair the response with your own renderer if you need a 3D mesh of either enantiomorph; this endpoint returns scalars and topology only and does not emit meshes, unit conversions, midradius, circumradius, or a chirality flag.
Where a snub dodecahedron calculator API earns its keep
CAD, digital-fabrication, and parametric-design notebooks often size Archimedean cells, quasi-spherical shells with high sphericity, or decorative chiral polyhedra; calling a tiny parse API avoids pulling a computer-algebra system for closed multiplications after a one-time Newton solve of the snub constant.
Technical questions
How do I compute snub dodecahedron volume and surface area?
Send a finite non-negative edge length as edge (aliases a, side, edge_length, length). The API returns volume, surface_area, faces, edges, vertices, and the closed formulas used.